## Reading List

Here are some books and papers that I found very helpful and particularly well written. Many of them are freely available.

**Algebraic Geometry:**Vakil's Notes*Foundations of Algebraic Geometry*, Harris*Algebraic Geometry*, Eisenbud & Harris*The Geometry of Schemes*, Shafarevich*Basic Algebraic Geometry 1***Homological algebra:**Kashiwara & Schapira*Sheaves on Manifolds*Chapter 1, Hilton & Stammbach*A Course in Homological Algebra***General Algebraic Topology:**Bott & Tu*Differential Forms in Algebraic Topology*, Aguilar, Gitler & Prieto:*Algebraic Topology from a Homotopical Viewpoint*, Davis & Kirk*Lecture Notes in Algebraic Topology*, May*A Concise Course in Algebraic Topology***Cobordism Theory:**Stong*Notes on Cobordism Theory***Smooth Manifolds:**Lee*Introduction to Smooth Manifolds*, Morita*Geometry of Differential Forms***Characteristic Classes:**Milnor & Stasheff*Characteristic Classes*, Hatcher*Vector Bundles and K-Theory***Riemann Surfaces:**Miranda*Algebraic Curves and Riemann Surfaces*, Forster*Lectures on Riemann Surfaces***Complex Geometry:**Huybrechts*Complex Geometry***Cyclic and Hochschild (Co)homology:**Kassel*Homology and cohomology of associative algebras***Lie & Algebraic Groups:**Bump*Lie Groups*, Tauvel & Yu*Lie Algebras and Algebraic Groups*, BrÃ¶cker & tom Dieck*Representations of Compact Lie Groups***Chern-Weil Theory:**Dupont*Fibre Bundles and Chern-Weil Theory*, Morita*Geometry of Differential Forms***Cohomology Operations:**Mosher, Tangora*Cohomology Operations and Applications in Homotopy Theory***Derived Categories:**Caldararu*Derived Categories of Sheaves*, Noohi*Lectures on derived and triangulated categories***Stacks:**Fantechi*Stacks for Everybody*, Metzler*Topological and Smooth Stacks*, Moerdijk*Introduction to the language of stacks and gerbes***Moduli spaces (e.g. stable curves):**Kock & Vainsencher*An Invitation to Quantum Cohomology***Simplicial Sets:**Riehl*A Leisurely Introduction to Simplicial Sets*-
**Simplicial Homotopy Theory and Model Categories:**Dwyer & Spalinski*Homotopy theories and model categories*, Goerss & Jardine*Simplicial Homotopy Theor*y **K-Theory:**Weibel*The K-Book*(algebraic K-Theory), Hatcher*Vector Bundles and K-Theory*(topological K-Theory), Rosenberg*Algebraic K-Theory and Its Applications***Surgery Theory:**Ranicki*Algebraic and Geometric Surgery***Simple-Homotopy Theory:**Milnor*Whitehead Torsion***Infinite Loop Spaces, Spectra, and Cohomology Theories:**Adams*Infinite Loop Spaces*, Adams*Stable Homotopy and Generalized Homology***PL Manifolds and Kirby-Siebenmann Theory:**Rudyak*Piecewise Linear Structures on Topological Manifolds***Galatius-Madsen-Weiss Theory:**Hatcher*A short exposition of the Madsen-Weiss theorem***Stable homology:**Church*Stable homology through scanning*