>>14200902List of useful math books
>First gradeAnalysis" by Laurent Schwartz, "Analysis" by Zorich,
"Problems and theorems from functional analysis" Kirillov-Gvishiani
Differential Topology (Milnor-Wallace),
Complex Analysis (Henri Cartan), Complex Analysis (Shabbat)
>Second courseLie groups and algebras (Serre)
Algebraic topology (Fuchs-Fomenko),
"Vector bundles and their applications" (Mishchenko)
"Characteristic Classes" (Milnor and Stashef)
Morse Theory (Milnor)
"Einstein Manifolds" (Arthur Besse),
Commutative Algebra (Atiyah-MacDonald),
Introduction to Algebraic Geometry (Mumford)
Algebraic Geometry (Griffiths and Harris),
Algebraic Geometry (Hartshorne)
Algebraic geometry (Shafarevich)
Algebraic Number Theory (eds. Cassels and Fröhlich)
Number theory (Borevich-Shafarevich)
Galois cohomology (Serre)
"Invariants of classical groups" (Hermann Weil)
>Third courseInfinite loop spaces (Adams)
K-theory (Atiyah)
Algebraic topology (Switzer)
Analysis (R. Wells)
Index formula (Atiyah-Bott-Patodi, collection of Mathematics)
Homological Algebra (Gelfand-Manin)
Group cohomology (Brown or something)
Cohomology of infinite-dimensional Lie algebras (Gelfand-Fuchs)
Kahlerian manifolds (André Weil)
Quasiconformal mappings (Alfors)
>Fourth year in collegeGeometric Topology (Sullivan)
Etale cohomology (Milne)
Algebraic geometry - review by Danilov (Algebraic Geometry 2, VINITI)
Chevalley groups (Steinberg)
Algebraic K-theory (Milnor)
Suslin's survey on algebraic K-theory from the 25th volume of VINITI
Multivariate Complex Analysis (Goto-Grosshans)
The same according to the book by Demaia (translation in preparation)
>Fifth yearGromov "Hyperbolic groups"
Gromov "Sign and geometric meaning of curvature"
