Resources for aspiring mathematical physicists
Basic online resources
MIT OpenCourseWare: Physics | Mathematics
The Feynman lectures in physics
t'Hooft's How to become a good theoretical physicist
David Tong: Lectures on Theoretical Physics
Leonard Susskind's Theoretical minimum
Perimeter Institute Recorded Seminar Archive: PIRSA
Note: For mathematical subjects mentioned in the links below, please refer to the MSC classification.
General references on "geometry and physics"
Introductory to intermediate
Jost, Geometry and physics
Fecko, Differential geometry and Lie groups for physicists
Isham, Modern differential geometry for physicists
Burke, Applied differential geometry
Bleecker, Gauge theory and variational principles
Baez and Muniain, Gauge fields, knots and gravity
Frankel, The geometry of physics
Hamilton, Mathematical gauge theory
Advanced
Boss and Bleecker, Topology and analysis: the Atiyah-Singer index formula and gauge-theoretic physics
Nash, Differential topology and quantum field theory
Dunajski, Solitons, instantons and twistors
Deligne et al, Quantum fields and strings: a course for mathematicians
Recommended books and articles by subject
Special and general relativity
Classical electrodynamics and classical field theory
Quantum field theory on curved spacetime
Some references for basic mathematical culture
Bourbaki, Elements de Mathematique
Rudin, Real and complex analysis
Taylor, Partial Differential Equations, vols. I-III
Hormander, The analysis of linear partial differential operators, vols. I-IV
Bredon, Topology and geometry
Spanier, Algebraic Topology
Spivak, A comprehensive introduction to differential geometry, vols. I-V
Kobayashi & Nomizu, Foundations of differential geometry
Besse, Einstein manifolds
Griffiths and Harris, Principles of algebraic geometry
Matsumura, Commutative ring theory
Mac Lane, Categories for the working mathematician