Идея украдена у euch. Я попытаюсь как-то упорядочить накопившиеся ссылки на разную литературу.

Algebraic geometry.
1. Why study algebraic geometry?
2. Best Algebraic Geometry text book? (other than Hartshorne)
3. Ravi Vakil, Foundations of Algebraic Geometry
4. The Stacks Project
5. Gortz, Wedhorn - Algebraic Geometry I
6. Derived Algebraic Geometry Reading List
7. Motives, Tannakian categories & Intersection Theory Reading List
8. Voevodsky et al, Motivic Homotopy Theory
*. Algebraic geometry, as seen by Andrei Tyurin

Basics of manifolds and differential geometry.
1. Introductory texts on manifolds
2. Brian Conrad, Differential Geometry handouts
3. Torstern Wedhorn, Manifolds, Sheaves and Cohomology, To be published in 2016
4. Yaiza Canzani, Analysis on manifolds via the Laplacian
5. A Spinorial Approach to Riemannian and Conformal Geometry
6. Course on Spin Geometry
6*. Other materials from Edinburgh Mathematical Physics Group
7. Vera Serganova, Lie groups
8. Jeff Viaclovsky, courses in differential geometry



Complex geometry
1. Learning complex geometry
1*. References for complex analytic geometry?
2. Jean-Pierre Demailly, Complex Analytic and Differential Geometry
3. Eberhard Freitag Lecture notes on Complex Spaces, Kahler manifolds, Hodge theory
4. Marco Manetti, Lectures on deformations of complex manifolds
5. Eleny Ionel, Complex Differential Geometry

Symplectic/contact geometry/topology
1. Contact geometry links

Representation theory
1. Dennis Gaitsgory, Geometric Representation Theory

Topology
1. Neil Strickland, A bestiary of topological objects
2. Allen Hatcher, Algebraic Topology, Vector Bundles and K-theory, Spectral Sequences, Topology of numbers
3. Peter May, A Concise Course in Algebraic Topology
3*. Peter May, More Concise Algebraic Topology
4. Ioannis Zois, 18 Lectures on K-theory
4*. K-theory texbook recommendations, MathOverflow
5. Notes on the Atiyah-Singer Thm, Liviu Nicolaescu

Mathematics around Physics
1. Kapustin, literature on Advanced Mathematical Methods of Physics
2. Peter Woit, Quantum Theory, Groups and Representations: An Introduction
2*.Peter Woit
3. Mirror Symmetry
4. Sheldon Katz
5. Denis Auroux, Topics in Mirror Symmetry
5.*Denis Auroux
6. IAS, Quantum Field Theory
7. NLab, Geometry of physics
7*. Urs Schreiber
8. Urs Schreiber, Differential cohomology in a cohesive topos
9. Frederic Paugam, Towards the mathematics of quantum field theory
10. Nick Sheridan, Mirror Symmetry stuff

Unsorted
1. Eckhard Meinrenken, Clifford Algebras and Lie Theory, recomended here
2. Marco Gualtieri, Dirac Geometry
3. Books of Dominic Joyce
4. Stiven Sivek, Contact geometry in 3 dimensions
5. Akhil Mathew's Notes from Harvard Courses
6. Jason Bland's Notes from Harvard Courses
7. Dan Freed, K-theory
7*. Dan Freed, Bordism: Old and New
7**. Classical Field Theory and Supersymmetry, Dan Freed
7***. Geometry of Dirac Operators, Dan Freed
7****. Dan Freed
8. Vaughan F.R. Jones, Von Neumann Algebras
9. Stephan Stolz, lecture notes
10. Tim Perutz, Topics in Floer theory
11. Sheel Ganatra, Aspects of Fukaya categories
12. Victor Ginzburg, Lectures on Noncommutative Geometry

Other lists:
1. Akhil Mathew
2. Maxim Stykow
3. Charles Siegel