Just like number theory, algebraic geometry applies algebra result to study geometry, blah, blah, blah. Algebraic geometry is related to algebra and number theory.
See Geometry & Topology Monographs for further study.
- Berger M., Pansu P., Berry J.-P. and Saint-Raymond X. Problems in Geometry
- Bredon G.E. Topology and Geometry
- Eves H. Survey of Geometry
- Coxeter H.S.M. Introduction to Geometry
- Hartshorne R. Geometry: Euclid and Beyond - He wrote an excellent text on algebraic geometry. Begin with this, see if you are with him.
- Hilbert D. The Foundations of Geometry (here for FREE!)
- Hilbert D. and Cohn-Vossen S. Geometry and the Imagination
- Hvidsten M. Geometry with Geometry Explorer - See the web for extra material.
- Nikulin V.V. and Shafarevich I.R. Geometries and Groups
- Bump D. Algebraic Geometry
- Dolgachev I.V. Introduction to Algebraic Geometry [.pdf] (FREE!)
- Dolgachev I.V. Topics in Classical Algebraic Geometry [.pdf] (FREE!)
- Drozd Y. Introduction to Algebraic Geometry [.pdf] (FREE!)
- Ewald G. Combinatorial Convexity and Algebraic Geometry
- Fulton W. Algebraic Curves: An Introduction to Algebraic Geometry
- Griffiths P. and Harris J. Principles of Algebraic Geometry
- Harris J. Algebraic Geometry: A First Course
- Hartshorne R. Algebraic Geometry (here is a scanned version for FREE!) - Solutions by William Stein, Richard Borcherds, Jinhyun Park and Chris [.pdf].
- Hassett B. Introduction to Algebraic Geometry
- Lang S. Introduction to Algebraic Geometry
- Lefschetz S. Algebraic Geometry
- Milne J.S. Algebraic Geometry (FREE!)
- Reid M. Undergraduate Algebraic Geometry
- Skorobogatov A.N. Algebraic Geometry Lecture Notes [.pdf] (FREE!)
- Smith K.E., Kahanpää L., Kekäläinen P. and Traves W. An Invitation to Algebraic Geometry
- Ueno K. An Introduction to Algebraic Geometry
- Walker R.J. Algebraic Curves
Further Algebraic Geometry:
- Basu S., Pollack R. and Roy M.-F. Algorithms in Real Algebraic Geometry
- Bochnak J., Coste M. and Roy M.-F. Real Algebraic Geometry
- Cox D.A., Little J.B. and O'Shea D.B. Using Algebraic Geometry - Don't forget to check out the typological error here.
- Debarre O. Higher-Dimensional Algebraic Geometry
- Eisenbud D. The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra
- Hirzebruch F. Topological Methods in Algebraic Geometry
- Lang S. Abelian Varieties (here is a scanned version for FREE!)
- Lang S. Introduction to Algebraic and Abelian Functions (here is a scanned version for FREE!)
- Le Potier J. Lectures on Vector Bundles
- Liu Q. Algebraic Geometry and Arithmetic Curves
- Mumford D. Abelian Varieties (here is a scanned version for FREE!)
- Reid M. Chapters on Algebraic Surfaces (FREE!)
- Semple J.G. and Kneebone G.T. Algebraic Projective Geometry
- Ueno K. Algebraic Geometry 1: From Algebraic Varieties to Schemes
Ueno K. Algebraic Geometry 2: Sheaves and Cohomology
Ueno K. Algebraic Geometry 3: Further Study of Schemes
- Voisin C. Hodge Theory and Complex Algebraic Geometry Vol 1, 2
- Yang K. Complex Algebraic Geometry
Also consult mathematical physics section below.
- Chern S.S. Chen W.H. and Lam K.S. Lectures on Differential Geometry - Basic topological concspts assumed. A chapter on Finsler geometry is added in the English translation.
- Eisenhart L.P. Transformations of Surfaces
- Helgason S. Differential Geometry, Lie Groups, and Symmetric Spaces
- Hwang A.D. Complex Manifolds and Hermitian Differential Geometry [.pdf] (FREE!)
- Ivey T.A. and Landsberg J.M. Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems
- Kennington A.U. Differential Geometry Reconstructed: A Unified Systematic Framework (FREE!) - Comprehensive.
- Kobayashi S. and Nomizu K. Foundations of Differential Geometry Vol 1, 2
- Kobayashi S. Transformation Groups in Differential Geometry
- Lang S. Fundamentals of Differential Geometry
- Lang S. Introduction to Differentiable Manifolds
- Lee J.M. Introduction to Topological Manifolds
- Madore K. An Introduction to Noncommutative Differential Geometry and its Physical Applications - More advanced work.
- Michor P.W. Topics in Differential Geometry [.pdf] (FREE!)
- Montiel S. and Ros A. Curves and Surfaces
- Schoen R. and Yau S.T. Lectures on Differential Geometry
- Spivak M. A Comprehensive Introduction to Differential Geometry 1, 2, 3, 4, 5 - An epic. Read the first two volumes at least. Content can be found here.
- Warner F.W. Foundations of Differentiable Manifolds and Lie Groups (here [.djvu] for FREE!)
- Boothby W.M. An Introduction to Differentiable Manifolds and Riemannian Geometry (here [.djvu] for FREE!)
- Chavel I. Riemannian Geometry: A Modern Introduction - Check the correction and addition [.pdf].
- Chern, S.S. and Shen Z. Riemann-Finsler Geometry
- do Carmo M.P. Riemannian Geometry
- Gallot S., Hulin D. and Lafontaine J. Riemannian Geometry
- Gudmundsson S. An Introduction to Riemannian Geometry (FREE!)
- Jost J. Riemannian Geometry and Geometric Analysis
- Lang S. Differential and Riemannian Manifolds
- Moller J.M. Riemannian Geometry [.pdf] (FREE!)
- O'Neill B. Semi-Riemannian Geometry With Applications to Relativity
- Petersen P. Riemannian Geometry
- Wilkins D.R. A Course in Riemannian Geometry [.pdf] (FREE!)
- Barnsley M.F. Fractals Everywhere
- Barnsley M.F. SuperFractals - See the web.
- Edgar G.A. Measure, Topology, and Fractal Geometry - See author's page for errata.
- Falconer K. Fractal Geometry: Mathematical Foundations and Applications
- Mandelbrot B.B. The Fractal Geometry of Nature
- Mörters P. Lecture Notes on Fractal Geometry [.ps] (FREE!)
- Peitgen H.-O., Jürgens H. and Saupe D. Chaos and Fractals: New Frontiers of Sciences (FREE!)
- Audin M. Geometry
- Bobenko A.I. and Suris Y.B. Discrete Differential Geometry: Consistency as Integrability (FREE!)
- Demailly J.-P. Complex Analytic and Differential Geometry [.pdf] (FREE!)
- Gruber P.M. Convex and Discrete Geometry
- Huybrechts D. Complex Geometry: An Introduction
- Jennings G.A. Modern Geometry with Applications
- Matousek J. Lectures on Discrete Geometry