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Geometry

There are various English-language editions of Euclid available at archive.org. Search here.

Euclidean

Introductory

• Euclid, tr. Heath. The Elements. Dover. (Vol I / Books 1-2, Vol II / Books 3-9, Vol III / Books 10-13)
• Euclid, tr. Heath. The Elements Green Lion Press. (Single volume)
• Lang and Murrow. Geometry: A High School Course (2e, Solutions manual)
• Kiselev and Givental. Kiselev’s Geometry (Vol I: Sumizdat 1e; Vol II: Sumizdat 1e) - Look for seller “sumizdat_dot_org”, that’s the publisher.
• Coxeter. Introduction to Geometry (Wiley 2e, 2e HC [OOP])
• Birkhoff and Beatley. Basic Geometry (AMS Chelsea ed, At AMS store; Manual for Teachers [at AMS store], Manual for Teachers [at AbeBooks]; Answer book [at AMS store], Answer Book [at AbeBooks])
• Brannan, Esplen, Gray. Geometry (2014, ISBN 978-1118679197, Worldcat, Amazon)
• Meyer. Geometry and Its Applications (2e, 2006: ISBN 978-0123694270, Worldcat, Amazon)

Beyond introductory

• Coxeter. Geometry Revisited (MAA 1967)
• Johnson. Advanced Euclidean Geometry (Dover)
• Casey, 1886. A Sequel to the First Six Books of the Elements of Euclid (At archive.org)
• Altshiller-Court. College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (2e Dover)
• Coxeter. Regular Polytopes (3e)

Euclidean and non-euclidean

• Hartshorne. Geometry: Euclid and Beyond (1e)
• Moise. Elementary Geometry From An Advanced Viewpoint (3e, 2e)
• Greenberg. Euclidean And Non-Euclidean Geometries (4e)
• Coxeter. Non-Euclidean Geometry (6e)
• Hilbert and Cohn-Vossen. Geometry and the Imagination (AMS Chelsea)
• Leonard, Lewis, Liu, Tokarsky. Classical Geometry: Euclidean, Transformational, Inversive, and Projective (1e 1997: ISBN 978-0760706602, Amazon; 2e 2003: ISBN 978-1592441303, Amazon)
• Stillwell. Numbers and Geometry (1e, 1997: ISBN 978-0387982892, Worldcat, Amazon)
• Stillwell. The Four Pillars of Geometry (1e 2005: ISBN 978-0387255309, Worldcat, Amazon)
• McDaniel. Geometry by Construction: Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries

Focusing on projective geometry

• Coxeter. Projective Geometry (2e)
• Cremona, 1885. Elements Of Projective Geometry (At archive.org)
• Meserve. Fundamental Concepts of Geometry (Dover)
• Veblen and Young. Projective Geometry (At archive.org: Vol 1, Vol 2, Search)

Computational Geometry

• de Berg, Cheong, van Kreveld, Overmars. Computational Geometry: Algorithms and Applications (3e)
• Edelsbrunner. A Short Course in Computational Geometry and Topology (1e)
• O’Rourke. Computational Geometry in C (2e)
• Cheng, Dey, Shewchuk. Delaunay Mesh Generation (1e)
• Botsch, Kobbelt, Pauly, Alliez, Levy. Polygon Mesh Processing Hardcover (1e)

General Topology

• Munkres. Topology (2e intl, 2e)

  The standard text. Also includes basic algebraic topology.

• Mendelson. Introduction to Topology (3e Dover)

  A brief introduction, available cheap.

• Gamelin and Greene. Introduction to Topology (2e Dover)

  Another cheap alternative. One of Alan Hatcher’s recommendations.

• Crossley. Essential Topology (1e corr)

  An introductory text with a reputation for easy reading.

• Willard. General Topology (Dover)

  Another affordable introduction. Maybe too much information for a true first book.

• Jänich. Topology (1e)

  Another of Alan Hatcher’s recommendations, he calls it “a pleasure to read.”

• Kelley. General Topology (At Archive.org, Springer hardcover 1975, Ishi Press 2008, Van Nostrand 1955)

  The classic introduction (1955).

• Simmons. Introduction to Topology and Modern Analysis (Krieger 2003)

• Croom. Principles of Topology (Dover)

  A gentle introduction for beginners.

• Prasolov. Intuitive Topology (1e)

  An extremely gentle introduction for extreme beginners.

• Steen and Seebach. Counterexamples in Topology (Dover)

• Henle. A Combinatorial Introduction to Topology

  Goes straight into algebraic topology with minimal coverage of point-set topology.

Algebraic Topology

• Hatcher. Algebraic Topology (f) (CUP Paperback, FREE ONLINE)
• Bredon. Topology and Geometry (1e)
• Stillwell. Classical Topology and Combinatorial Group Theory (2e)
• Rotman. An Introduction to Algebraic Topology (1e)
• Fulton. Algebraic Topology: A First Course (1e)
• May. A Concise Course in Algebraic Topology (1e)
• May and Ponto. More Concise Algebraic Topology: Localization, Completion, and Model Categories (1e)
• Lee. Introduction to Topological Manifolds (2e)

Differential Geometry

• Pressley. Elementary Differential Geometry (2e/2010)
• Tu. An Introduction to Manifolds (2e/2011)
• Guillemin and Pollack. Differential Topology (AMS Chelsea)
• Millman and Parker. Elements of Differential Geometry (1e)
• O’Neill. Elementary Differential Geometry (2e)
• Milnor. Topology from the Differentiable Viewpoint (PUP revised)
• Kreyszig. Differential Geometry (Dover)
• Spivak. A Comprehensive Introduction to Differential Geometry (in 6 volumes) (Vol I, 3e; Vol II, 3e; etc.)
• Guggenheimer. Differential Geometry (Dover)
• Bishop & Goldberg. Tensor Analysis on Manifolds (Dover)
• Lee. Introduction to Smooth Manifolds (1e)
• Lee. Riemannian Manifolds: An Introduction to Curvature (1e)
• Do Carmo. Riemannian Geometry (1e)
• Do Carmo. Differential Geometry of Curves and Surfaces (2e Dover, 1e)
• Matsumoto. An Introduction to Morse Theory (1e)
• Kosinski. Differential Manifolds (Dover)
• Lovelock and Rund. Tensors, Differential Forms, and Variational Principles (Dover)
• Struik. Lectures on Classical Differential Geometry (Dover)
• McInerney. First Steps in Differential Geometry: Riemannian, Contact, Symplectic
• Tapp. Differential Geometry of Curves and Surfaces

Applied and Computational Topology

• Ghrist. Elementary Applied Topology (At CreateSpace, At Amazon)
• Edelsbrunner and Harer. Computational Topology: An Introduction (1e)
• Zomorodian. Topology for Computing (1e)
• Kaczynski, Mischaikow, Mrozek. Computational Homology (1e)

Algebraic geometry

Introductions

• Beltrametti, Carletti, Gallarati, Bragadin. Lectures on Curves, Surfaces and Projective Varieties (1e)
• Garrity et al. Algebraic Geometry: A Problem Solving Approach (1e)
• Shafarevich, Reid. Basic Algebraic Geometry 1: Varieties in Projective Space (3e)
• Shafarevich, Reid. Basic Algebraic Geometry 2: Schemes and Complex Manifolds (3e)
• Holme. A Royal Road to Algebraic Geometry (1e)
• Fulton. Algebraic Curves, an Introduction to Algebraic Geometry
• Gathmann. Algebraic Geometry (SS 2014)
• Smith, 2014. Introduction to Algebraic Geometry (1e Paperback, FREE ONLINE)
• Vakil. The Rising Sea: Foundations Of Algebraic Geometry Notes (main page, blog, Ravi Vakil’s homepage)

Classical (pre-Grothendieck)

• Lang, 1958. Introduction to Algebraic Geometry (Martino)
• Weil, 1946, 1962. Foundations of algebraic geometry ()
• Lefschetz, 1953. Algebraic Geometry (Dover)
• Hodge and Pedoe, 1947. Methods of Algebraic Geometry (Vol I, Vol II, Vol III)
• Baker, 1922-1925. Principles of Geometry (At archive.org: Vol 1, Vol 2, Vol 3, Vol 4, Vol 5, Vol 6)

Beyond

• Hartshorne. Algebraic Geometry (1e)
• Liu. Algebraic Geometry and Arithmetic Curves (1e
• Griffiths, Harris. Principles of Algebraic Geometry (Intl ed @AbeBooks)
• Görtz, Wedhorn. Algebraic Geometry I, Schemes with Examples and Exercises (1e)
• Vakil. The Rising Sea: Foundations Of Algebraic Geometry Notes
• Eisenbud and Harris. 3264 and All That: A Second Course in Algebraic Geometry (1e)