A graduate level Quantum Mechanics course, by Prof. Cumrun Vafa.
A course on Black Holes, by Prof. Andrew Strominger.
An introductory course on String Theory (without requiring knowledge of QFT), by Prof. Paul Townsend
A lightning revision of a first course in QFT, in preparation for loops and renormalisation.
Notes on the path-integral, including the basics and some tricks.
Now, everything below is relevant to some theoretical physics courses of Cambridge University’s Part III of the Mathematical Tripos. Please use them with caution, and as references only: some are (intentionally) left incomplete, and there can certainly be mistakes.
Below are the past January DAMTP early PhD admission exams.
The past exam papers can be found here. Below are some of the solutions to past exams.
Symmetries, Particles, Fields: 2013.
String Theory: 2013.
Note that I often changed conventions to match 2013-14 lecturers' conventions. In writing the solutions, I have made use of the lecture notes of the corresponding years.
Here are some collections of definitions in differential geometry from my Symmetries (Nicolas Manton), General Relativity (Harvey Reall) and Applications of Differential Geometry (Maciej Dunajski) courses. These are not intended for mathematicians… :P
And below are some quick and random problems I set for myself while reviewing for exams. Most of the solutions can be found in the lecture notes of the corresponding courses.