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This is a section of the Basic Math Library List. Please help to improve the article.


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The subject description:

5. Geometry 
   Local and global differential geometry. Geometric PDE and geometric flows. Geometric structures on manifolds. 
   Riemannian and metric geometry. Geometric aspects of group theory. Convex geometry. Discrete geometry. 
   Geometric rigidity.
   Connections with sections 2, 4, 6, 7, 8, 9, 10, 11, 12.


  • Please define a better classifications on this subject.


Tags: (Use similar tags to highlight your recommendations.)

  • Essential and Recommended for the selected books on the final list.
  • ***, ** and * for books recommended by MAA's list.
  • MR for books with positive reviews in MathSciNet.
  • MN for books recommended by BMLL.



Elementary Geometry

Geometry: General

*** Banchoff, Thomas F. Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions New York, NY: Scientific American Library, 1990.

Blackwell, William. Geometry in Architecture New York, NY: John Wiley, 1984.

Bold, Benjamin. Famous Problems of Geometry and How to Solve Them Mineola, NY: Dover, 1982.

Burger, Dionys. Sphereland New York, NY: Thomas Y. Crowell, 1965.

** Croft, Hallard T.; Falconer, Kenneth J.; and Guy, Richard K. Unsolved Problems in Geometry New York, NY: Springer-Verlag, 1991.

* Fischer, Gerd, ed. Mathematical Models from the Collections of Universities and Museums, Wiesbaden: Friedr. Vieweg and Sohn, 1986. 2 Vols.

** Friedrichs, Kurt Otto. From Pythagoras to Einstein Washington, DC: Mathematical Association of America, 1965.

*** Hilbert, David and Cohn-Vossen, S. Geometry and the Imagination New York, NY: Chelsea, 1952.

*** Hildebrandt, Stefan and Tromba, Anthony J. Mathematics and Optimal Form New York, NY: Scientific American Library, 1984.

Ivins, William M., Jr. Art and Geometry: A Study in Space Intuitions Mineola, NY: Dover, 1964.

** Krause, Eugene F. Taxicab Geometry: An Adventure in Non-Euclidean Geometry Mineola, NY: Dover, 1986.

Lord, E.A. and Wilson, C.B. The Mathematical Description of Shape and Form New York, NY: Halsted Press, 1984.

March, Lionel and Steadman, Philip. The Geometry of Environment: An Introduction to Spatial Organization in Design Cambridge, MA: MIT Press, 1974.

Pottage, John. Geometrical Investigations: Illustrating the Art of Discovery in the Mathematical Field Reading, MA: Addison-Wesley, 1983.

* Row, T. Sundara. Geometric Exercises in Paper Folding Mineola, NY: Dover, 1966.

Rucker, Rudy. Geometry, Relativity, and the Fourth Dimension Mineola, NY: Dover, 1977.

* Stewart, Bonnie M. Adventures Among the Toroids, 4494 Wasau Road, Okemos, MI: 1970, 1980. Second Edition.


Geometry: Surveys

* Berger, Marcel, et al. Problems in Geometry New York, NY: Springer-Verlag, 1984.

* Berger, Marcel. Geometry, New York, NY: Springer-Verlag, 1987. 2 Vols.

* Cederberg, Judith N. A Course in Modern Geometries New York, NY: Springer-Verlag, 1989.

Court, Nathan A. College Geometry, New York, NY: Barnes and Noble, 1952. Second Edition.

Cox, Philip L. Geometry in Easy Steps: An Informal Approach Needham Heights, MA: Allyn and Bacon, 1983.

*** Coxeter, H.S.M. Introduction to Geometry, New York, NY: John Wiley, 1969. Second Edition.

*** Eves, Howard W. A Survey of Geometry, Boston, MA: Allyn and Bacon, 1972. Second Revised Edition.

Lial, Margaret L.; Steffensen, Arnold R.; and Johnson, L. Murphy. Essentials of Geometry for College Students Glenview, IL: Scott Foresman, 1990. * Melzak, Z.A. Invitation to Geometry New York, NY: John Wiley, 1983.

* Millman, Richard S. and Parker, George D. Geometry: A Metric Approach with Models, New York, NY: Springer-Verlag, 1981, 1991. Second Edition.

* Pedoe, Dan. Geometry and the Visual Arts Mineola, NY: Dover, 1983. (Former title: Geometry and the Liberal Arts.)

Pedoe, Dan. Geometry: A Comprehensive Course Mineola, NY: Dover, 1988. (Former title: A Course of Geometry for Colleges and Universities.)

Postnikov, Mikhail. Lectures in Geometry, Moscow: MIR, 1982, 1986. 2 Vols.

Prenowitz, Walter and Jordan, M. Basic Concepts of Geometry New York, NY: John Wiley, 1965.

Smart, James R. Modern Geometries, Pacific Grove, CA: Brooks/Cole, 1973, 1988. Third Edition.

** Stehney, Ann K., et al., eds. Selected Papers on Geometry Washington, DC: Mathematical Association of America, 1979.

Tuller, Anita. A Modern Introduction to Geometries New York, NY: Van Nostrand Reinhold, 1967.


School Geometry

* Bruni, James V. Experiencing Geometry Belmont, CA: Wadsworth, 1977.

Clemens, Stanley R.; O'Daffer, Phares G.; and Clooney, Thomas J. Geometry Reading, MA: Addison-Wesley, 1983.

* Fetisov, A.I. Proof in Geometry Moscow: MIR, 1978.

Hoffer, Alan. Geometry Reading, MA: Addison-Wesley, 1979.

** Jacobs, Harold R. Geometry, New York, NY: W.H. Freeman, 1974, 1986. Second Edition.

Kempe, A.B. How to Draw a Straight Line Reston, VA: National Council of Teachers of Mathematics, 1977.

* Konkle, Gail S. Shapes and Perceptions: An Intuitive Approach to Geometry Boston, MA: Prindle, Weber and Schmidt, 1974.

Loomis, E. The Pythagorean Proposition Reston, VA: National Council of Teachers of Mathematics, 1968.

* Moise, Edwin E. and Downs, Floyd L. Geometry Reading, MA: Addison-Wesley, 1975.

** O'Daffer, Phares G. and Clemens, Stanley R. Geometry: An Investigative Approach Reading, MA: Addison-Wesley, 1976.


Euclidean and Non-Euclidean Geometry

Beskin, N.M. Dividing a Segment in a Given Ratio Moscow: MIR, 1975.

* Coxeter, H.S.M. Non-Euclidean Geometry Toronto: University of Toronto Press, 1957.

*** Coxeter, H.S.M., et al. Geometry Revisited Washington, DC: Mathematical Association of America, 1967.

* Dudley, Underwood. A Budget of Trisections New York, NY: Springer-Verlag, 1987.

* Faber, Richard L. Foundations of Euclidean and Non-Euclidean Geometry New York, NY: Marcel Dekker, 1983.

* Gans, David. An Introduction to Non-Euclidean Geometry New York, NY: Academic Press, 1973.

** Gray, Jeremy. Ideas of Space: Euclidean, Non-Euclidean, and Relativistic, New York, NY: Clarendon Press, 1979, 1989. Second Edition.

* Greenberg, Marvin Jay. Euclidean and Non-Euclidean Geometries: Development and History New York, NY: W.H. Freeman, 1974, 1980.

*** Hilbert, David. The Foundations of Geometry, La Salle, IL: Open Court, 1962, 1971. Tenth Edition.

Kelly, Paul J. and Matthews, Gordon. The Non-Euclidean, Hyperbolic Plane: Its Structure and Consistency New York, NY: Springer-Verlag, 1981.

Kogan, B. Yu. The Application of Mechanics to Geometry Chicago, IL: University of Chicago Press, 1974.

Lobachevski, N. The Theory of Parallels Peru, IL: Open Court, 1914.

* Martin, George E. The Foundations of Geometry and the Non-Euclidean Plane New York, NY: Springer-Verlag, 1975.

Moise, Edwin E. Elementary Geometry from an Advanced Standpoint, Reading, MA: Addison-Wesley, 1974. Second Edition.

Morley, F. and Morley, F.M. Inversive Geometry New York, NY: Chelsea, 1954.

Nikulin, V.V. and Shafarevich, Igor R. Geometries and Groups New York, NY: Springer-Verlag, 1987.

Pedoe, Dan. Circles: A Mathematical View Mineola, NY: Dover, 1979.

Posamentier, Alfred S. Excursions in Advanced Euclidean Geometry Reading, MA: Addison-Wesley, 1984.

Rosenfeld, B.A. and Sergeeva, N.D. Stereographic Projection Moscow: MIR, 1977.

Ryan, Patrick J. Euclidean and Non-Euclidean Geometry: An Analytical Approach New York, NY: Cambridge University Press, 1986.

Schwerdtfeger, Hans. Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry Mineola, NY: Dover, 1979.

Shreider, Yu. A. What is Distance? Chicago, IL: University of Chicago Press, 1974.

* Szmielew, Wanda. From Affine to Euclidean Geometry: An Axiomatic Approach Norwell, MA: D. Reidel, 1983.

Trudeau, Richard J. The Non-Euclidean Revolution New York, NY: Birkhauser, 1987.

Vaisman, Izu. Foundations of Three-Dimensional Euclidean Geometry New York, NY: Marcel Dekker, 1980.

Yaglom, I.M. A Simple Non-Euclidean Geometry and Its Physical Basis New York, NY: Springer-Verlag, 1979.

* Yates, Robert C. The Trisection Problem Reston, VA: National Council of Teachers of Mathematics, 1971.


Polyhedra, Tilings, Symmetry

** Armstrong, M.A. Groups and Symmetry New York, NY: Springer-Verlag, 1988.

* Baglivo, Jenny A. and Graver, Jack E. Incidence and Symmetry in Design and Architecture New York, NY: Cambridge University Press, 1983.

Beskin, N.M. Images of Geometric Solids Moscow: MIR, 1985.

* Bunch, Bryan H. Reality's Mirrors: Exploring the Mathematics of Symmetry New York, NY: John Wiley, 1989.

Coxeter, H.S.M. Regular Polytopes, Mineola, NY: Dover, 1973. Third Edition.

* Coxeter, H.S.M., et al., eds. M.C. Escher: Art and Science New York, NY: Elsevier Science, 1986.

** Cundy, M.H. and Rollett, A.P. Mathematical Models New York, NY: Clarendon Press, 1961.

*** Grunbaum, Branko and Shephard, G.C. Tilings and Patterns New York, NY: W.H. Freeman, 1986, 1989.

* Grunbaum, Branko. Convex Polytopes New York, NY: John Wiley, 1967.

Hargittai, Istvan, ed. Symmetry: Unifying Human Understanding Elmsford, NY: Pergamon Press, 1986.

* Henderson, Linda D. The Fourth Dimension and Non-Euclidean Geometry in Modern Art Princeton, NJ: Princeton University Press, 1983.

* Hilton, Peter J. and Pedersen, Jean. Build Your Own Polyhedra Reading, MA: Addison-Wesley, 1988.

* Holden, Alan. Shapes, Space, and Symmetry New York, NY: Columbia University Press, 1971.

Holden, Alan. Orderly Tangles: Cloverleafs, Gordian Knots, and Regular Polylinks New York, NY: Columbia University Press, 1983.

Kavanau, J. Lee. Symmetry: An Analytical Treatment West Los Angeles, CA: Science Software Systems, 1980.

* Lockwood, E.H. and Macmillan, R.H. Geometric Symmetry New York, NY: Cambridge University Press, 1978.

Loeb, Arthur L. Space Structures: Their Harmony and Counterpoint Reading, MA: Addison-Wesley, 1976.

Loeb, Arthur L. Color and Symmetry New York, NY: John Wiley, 1971.

Lyndon, Roger C. Groups and Geometry New York, NY: Cambridge University Press, 1985.

MacGillavry, Caroline H. Fantasy Symmetry: The Periodic Drawings of M.S. Escher New York, NY: Harry N. Abrams, 1976.

* Martin, George E. Transformation Geometry: An Introduction to Symmetry New York, NY: Springer-Verlag, 1982.

Pearce, Peter and Pearce, Susan. Polyhedra Primer New York, NY: Van Nostrand Reinhold, 1978.

Pugh, Anthony. Polyhedra: A Visual Approach Berkeley, CA: University of California Press, 1976.

Ranucci, E.R. and Teeters, J.L. Creating Escher-Type Drawings Palo Alto, CA: Creative Publ., 1977.

* Rosen, Joe. Symmetry Discovered: Concepts and Applications in Nature and Science New York, NY: Cambridge University Press, 1975.

** Schattschneider, Doris J. Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M.C. Escher New York, NY: W.H. Freeman, 1990.

* Senechal, Marjorie and Fleck, George, eds. Patterns of Symmetry Amherst, MA: University of Massachusetts Press, 1977.

** Senechal, Marjorie and Fleck, George, eds. Shaping Space: A Polyhedral Approach New York, NY: Birkhauser, 1988.

Shubnikov, A.V. and Koptsik, V.A. Symmetry in Science and Art New York, NY: Plenum Press, 1974.

Stevens, Peter S. Patterns in Nature Waltham, MA: Little, Brown, 1974.

* Toth, L. Fejes. Regular Figures Elmsford, NY: Pergamon Press, 1964.

Wenninger, Magnus J. Spherical Models New York, NY: Cambridge University Press, 1979.

* Wenninger, Magnus J. Polyhedron Models New York, NY: Cambridge University Press, 1971.

*** Weyl, Hermann. Symmetry Princeton, NJ: Princeton University Press, 1952.


Geometric Transformations

* Bakel'man, I. Ya. Inversions Chicago, IL: University of Chicago Press, 1974.

Eccles, Frank M. An Introduction to Transformational Geometry Reading, MA: Addison-Wesley, 1971.

* Gans, David. Transformations and Geometries Englewood Cliffs, NJ: Appleton-Century-Crofts, 1969.

** Yaglom, I.M. Geometric Transformations, Washington, DC: Mathematical Association of America, 1962--73. 3 Vols.


Projective Geometry

* Blumenthal, Leonard M. Modern View of Geometry Mineola, NY: Dover, 1980.

** Coxeter, H.S.M. Projective Geometry, Toronto: University of Toronto Press, 1974. Second Edition.

* Coxeter, H.S.M. The Real Projective Plane New York, NY: Cambridge University Press, 1961.

Dorwart, Harold L. Geometry of Incidence Englewood Cliffs, NJ: Prentice Hall, 1966.

Fishback, William T. Projective and Euclidean Geometry, New York, NY: John Wiley, 1969. Second Edition.

Garner, Lynn E. An Outline of Projective Geometry Amsterdam: North-Holland, 1981.

Hirschfeld, J.W.P. Projective Geometries Over Finite Fields New York, NY: Clarendon Press, 1979.

Hirschfeld, J.W.P. Finite Projective Spaces of Three Dimensions New York, NY: Clarendon Press, 1985.

Penna, Michael A. and Patterson, Richard R. Projective Geometry and Its Applications to Computer Graphics Englewood Cliffs, NJ: Prentice Hall, 1986.

Samuel, Pierre. Projective Geometry New York, NY: Springer-Verlag, 1988.

* Veblen, Oswald and Young, John Wesley. Projective Geometry, New York, NY: Blaisdell, 1938, 1946. 2 Vols.

Wylie, Clarence R. Introduction to Projective Geometry New York, NY: McGraw-Hill, 1970.

* Young, John Wesley. Projective Geometry Washington, DC: Mathematical Association of America, 1930.


Computational Geometry

** Abelson, Harold and diSessa, Andrea A. Turtle Geometry: The Computer as a Medium for Exploring Mathematics Cambridge, MA: MIT Press, 1981.

Billstein, Rick; Libeskind, S.; and Lott, Johnny W. Logo Redwood City, CA: Benjamin Cummings, 1985.

Clayson, J. Visual Modeling with Logo Cambridge, MA: MIT Press, 1988.

Edelsbrunner, H. Algorithms in Computational Geometry New York, NY: Springer-Verlag, 1987.

** O'Rourke, Joseph. Art Gallery Theorems and Algorithms New York, NY: Oxford University Press, 1987.

* Preparata, Franco P. and Shamos, Michael I. Computational Geometry: An Introduction New York, NY: Springer-Verlag, 1985.

Toussaint, G., ed. Computational Geometry Amsterdam: North-Holland, 1985.


Discrete and Combinatorial Geometry

Ambartzumian, R.V. Combinatorial Integral Geometry with Applications to Mathematical Stereology New York, NY: John Wiley, 1982.

Batten, Lynn Margaret. Combinatorics of Finite Geometries New York, NY: Cambridge University Press, 1986.

* Boltyanskii, Vladimir G. Equivalent and Equidecomposable Figures Lexington, MA: D.C. Heath, 1963.

** Boltyanskii, Vladimir G. Hilbert's Third Problem Silver Spring, MD: V.H. Winston, 1978.

* Boltyanskii, Vladimir G. and Gohberg, Israel. The Decomposition of Figures into Smaller Parts Chicago, IL: University of Chicago Press, 1980.

* Boltyanskii, Vladimir G. and Gohberg, Israel. Results and Problems in Combinatorial Geometry New York, NY: Cambridge University Press, 1985.

** Bonnesen, T. and Fenchel, W. Theory of Convex Bodies Moscow, ID: BCS Associates, 1987.

* Hadwiger, Hugo and Debrunner, Hans. Combinatorial Geometry in the Plane New York, NY: Holt, Rinehart and Winston, 1964.

** Kazarinoff, Nicholas D. Geometric Inequalities Washington, DC: Mathematical Association of America, 1961, 1975.

Kelly, Paul J. and Weiss, Max L. Geometry and Convexity: A Study in Mathematical Methods New York, NY: John Wiley, 1979.

** Lay, Steven R. Convex Sets and Their Applications New York, NY: John Wiley, 1982.

* Ledermann, Walter and Vajda, Steven, eds. Geometry and Combinatorics New York, NY: John Wiley, 1985. Handbook of Applicable Mathematics, Volume V.

** Mitrinovic, Dragoslav S.; Pe caric, J.E.; and Volenec, V. Recent Advances in Geometric Inequalities Norwell, MA: Kluwer Academic, 1989.

Moser, William. Problems in Discrete Geometry, Toronto: McGill-Queen's University Press, 1979, 1980. Fifth Edition.

Prenowitz, Walter and Jantosciak, James. Join Geometries: A Theory of Convex Sets and Linear Geometry New York, NY: Springer-Verlag, 1979.

* Yaglom, I.M. and Boltyanskii, Vladimir G. Convex Figures New York, NY: Holt, Rinehart and Winston, 1961.


More ...

J. Roe, "Elementary Geometry".


M. Berger, "Geometry I,II" (two volumes).


Differential Geometry

Abraham, R., Marsden, J. E., Ratiu, T., Manifolds, tensor analysis, and applications. Second edition. Applied Mathematical Sciences, 75. Springer-Verlag, New York, 1988. x+654 pp. \$59.80. ISBN 0-387-96790-7


* Arnold, V.I. Catastrophe Theory, New York, NY: Springer-Verlag, 1984, 1986. Second Edition.

Berger, Marcel and Gostiaux, Bernard. Differential Geometry: Manifolds, Curves, and Surfaces New York, NY: Springer-Verlag, 1988.

* Boothby, William M. An Introduction to Differentiable Manifolds and Riemannian Geometry, New York, NY: Academic Press, 1975, 1986. Second Edition.

* Burke, William L. Applied Differential Geometry New York, NY: Cambridge University Press, 1985.

* Dodson, C.T.J. and Poston, Tim. Tensor Geometry: The Geometric Viewpoint and its Uses Brooklyn, NY: Pitman, 1977.

Faber, Richard L. Differential Geometry and Relativity Theory: An Introduction New York, NY: Marcel Dekker, 1983.

Flanders, Harley. Differential Forms with Applications to the Physical Sciences Mineola, NY: Dover, 1989.

Hopf, Heinz. Differential Geometry in the Large New York, NY: Springer-Verlag, 1983.

** Hsiung, Chuan-Chih. A First Course in Differential Geometry New York, NY: John Wiley, 1981.

Kahn, Donald W. Introduction to Global Analysis New York, NY: Academic Press, 1980.

* Kobayashi, Shoshichi and Nomizu, Katsumi. Foundations of Differential Geometry, New York, NY: John Wiley, 1963--69. 2 Vols.

Lu, Yung-Chen. Singularity Theory and an Introduction to Catastrophe Theory New York, NY: Springer-Verlag, 1976.

Marmo, Giuseppe, et al. Dynamical Systems: A Differential Geometric Approach to Symmetry and Reduction New York, NY: John Wiley, 1985.

* Millman, Richard S. and Parker, George D. Elements of Differential Geometry Englewood Cliffs, NJ: Prentice Hall, 1977.

O'Neill, Barrett. Elementary Differential Geometry New York, NY: Academic Press, 1966.

** Spivak, Michael D. A Comprehensive Introduction to Differential Geometry, Boston, MA: Publish or Perish, 1970--79. Second Edition,

Stoker, J.J. Differential Geometry New York, NY: John Wiley, 1969.

** Struik, Dirk Jan. Lectures on Classical Differential Geometry, Mineola, NY: Dover, 1988. (Former title: Differential Geometry.)

Thorpe, John A. Elementary Topics in Differential Geometry New York, NY: Springer-Verlag, 1979.

Veblen, Oswald and Whitehead, J.H.C. The Foundations of Differential Geometry New York, NY: Cambridge University Press, 1967.

** do Carmo, Manfredo P. Differential Geometry of Curves and Surfaces Englewood Cliffs, NJ: Prentice Hall, 1976.

McDuff, Dusa(1-SUNYS); Salamon, Dietmar(4-WARW-MI) Introduction to symplectic topology. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. viii+425 pp. \$82.00. ISBN 0-19-851177-9 Moved to Topology section.

Cannas da Silva, Ana(P-TULT) Lectures on symplectic geometry. Lecture Notes in Mathematics, 1764. Springer-Verlag, Berlin, 2001. xii+217 pp. \$45.80. ISBN 3-540-42195-5 Moved to Topology section.


Special Topics

Artzy, Rafael. Linear Geometry Reading, MA: Addison-Wesley, 1974.

* Dembowski, P. Finite Geometries New York, NY: Springer-Verlag, 1968.

Edmondson, Amy C. A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller New York, NY: Birkhauser, 1987.

Gordon, V.O. and Sementsov-Ogievskii, M.A. A Course in Descriptive Geometry Moscow: MIR, 1980.

Hammer, J. Unsolved Problems Concerning Lattice Points Brooklyn, NY: Pitman, 1977.

Hughes, D.R. and Piper, F.C. Design Theory, New York, NY: Cambridge University Press, 1985, 1988. Second Edition.

** Lockwood, E.H. A Book of Curves New York, NY: Cambridge University Press, 1960.

Lyusternik, L.A. The Shortest Lines: Variational Problems Moscow: MIR, 1976, 1983.

* Mortenson, Michael E. Geometric Modeling New York, NY: John Wiley, 1985.

Porteous, Ian R. Topological Geometry, New York, NY: Cambridge University Press, 1981. Second Edition.

Pugh, Anthony. An Introduction to Tensegrity Berkeley, CA: University of California Press, 1976.

Santalo, Luis A. Integral Geometry and Geometric Probability Reading, MA: Addison-Wesley, 1976.

Schuster, Seymour. Elementary Vector Geometry New York, NY: John Wiley, 1962.

* Snapper, Ernst and Troyer, Robert J. Metric Affine Geometry Mineola, NY: Dover, 1989.

* Yates, Robert C. Curves and Their Properties Reston, VA: National Council of Teachers of Mathematics, 1974.

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