I'm a university student of theoretical physics and mathematics, whilst my own studies focus on gravitational physics (e.g. string theory), differential geometry, and gauge field theories.
- Quantum Field Theory: http://www.damtp.cam.ac.uk/user/tong/qft.html; Introduction to Quantum Field Theory by Peskin and Schroeder
- String Theory: http://www.damtp.cam.ac.uk/user/tong/string.html; String Theory and M-Theory by Becker, Becker and Schwarz; Superstring Theory by Witten; String Theory, course by Prof. Freddy Chachazo, available at: http://perimeterscholars.org/
- Solitons, Topology: Classical Solutions in Quantum Field Theory by Weinberg; http://www.damtp.cam.ac.uk/user/tong/tasi.html
- Advanced General Relativity: Gravitational Physics, course by Prof. Ruth Gregory, video lectures available at: http://perimeterscholars.org/
- Advanced Differential Geometry: A Brief Introduction to Characteristic Classes from the Differential Viewpoint (Free Notes) by Yang Zhang, Cornell University
- Calabi-Yau Manifolds: A Bestiary for Physicists by T. Hubsch; an introduction to Calabi-Yau manifolds meant to be accessible to physicists, but requires a substantial background in some algebraic and differential geometry.
- Mannheim's Brane-Localized Gravity; discusses branes and fields in the context of general relativity, explicit computations are present throughout, in great detail.
- All volumes of A Comprehensive Introduction to Differential Geometry by Spivak; thorough, excellently written and with great insights.
Profile image: an artist's depiction of a two-dimensional slice of a Calabi-Yau manifold, which by definition has vanishing first Chern class or equivalently trivial canonical bundle.
Nullius in verba