During the course of my studies I have realized how invaluable a well written set of lecture notes can be. Good lecture notes mean you learn the material well, faster and easier. This doesn’t mean however that the notes are easy or that they dumb down the subject, not at all.
Here I collect lecture notes and resources which I have found to be valuable (if I have studied from them) or that struck me as well written and which I plan to read at some point. I must recognize I was somewhat inspired by Gerard ‘t Hooft’s website How to become a good Theoretical Physicist and I encourage you to visit it.
I try to divide when possible by subject but, especially for advanced topics, they tend to mix a little. You will also find links to other collections of notes. I will try to follow an order of increasing difficulty, which can be useful to fellow students. The notes are mostly of “graduate” level and forwards, basically meaning from the 4th year of physics education onwards.
Finally, the following are ultimately the opinions of a student, not of a theoretical physicist so even if I try my best to give an informative assessment of these resources based on my experience, it is rather probable that I will make some wrong or inaccurate or biased considerations. Please do reach out with any constructive criticism you might have, I will appreciate it!
QFT
• David Tong's introductory QFT notes.
They are a great place to start if you haven't encountered QFT yet. A third year student with good knowledge of QM should find them accesible. A complementary book of roughly the same level is the one by Maggiore with the bonus of quite a few worked examples and solved problems.
• Solutions to Peskin and Schroeder by Zhong-Zhi Xianyu.
Exercises, I believe, are the backbone of a physicist's education and one should spend at least as much time doing exercises as reading the theory. Solutions to problems are then a great asset if used correctly. Although I haven't studied much from P&S, I have used it for the problems and the combination with these solutions probably make it the best place to study the fundamentals of QFT from.
• Brando Bellazzini and Stephane Lavignac's QFT II course at ENS.
I really enjoyed this course and Brando's website contains notes for all of his lectures, exercise sessions and homework problems (with solutions). The notes are handwritten but very readable, the homework is in Latex and so are the solutions. The course's two main topics are non abelian gauge theories and spontaneous symmetry breaking. Brando was often original and did not follow a textbook which makes his notes quite valuable.
• SISSA's PhD courses QFT I by Marco Serone and QFT II by Roberto Percacci.
SISSA's PhD courses are in general very good (notes-wise at least). It's worth checking out the Theoretical Particle Physics (TPP), the AstroParticle Physics (APP) and the Statistical Physics groups for useful material (and cool research!).
The QFT I notes are very good, covering in depth all the fundamental topics of QFT (have a look at the index!). All the techniques developed are then put to use in a final study of the Abelian Higgs model. Definitely notes to master if one wants to have a solid knowledge of field theory, especially for high energy applications.
The QFT II notes cover some "advanced" topics like solitons, instantons and all that and they give a more advanced treatment of anomalies than the QFT I lectures along with critical phenomena and other things. They are the best notes I have found that treat these topics in a cohesive way (if you know better, please tell me!).
• David Tong's notes on Gauge Theory.
GR
• David Tong's GR notes
These are quite new but, as always with Tong, they are excellent to approach the subject and they also start to cover some more advanced topics. Definitely good place to start. A good complementary book for the basics is Schutz's 'A first course in General Relativity'.
• Harvey Reall's notes on GR and black holes
Reall's notes on GR are also an excellent starting point. They are a bit more formal than Tong's and cover slightly different topics. My reccomendation would be to read a bit of both and then decide which suits you best and stick to it. His notes on black holes are also very good and formal. In particular, they cover the initial value problem and singularity theorems. Many parts are structured as math books with definitions, propositions and theorems.
• Paul Townsends's notes on black holes
Tonwsend's historical notes on black holes are a standard reference and very good for students who want to get into it. He does not cover singularity theorems like Reall though. Again, check both his notes and Reall's and decide what is best for your objectives. Personally, I enjoy better Townsend's style.
• Geoffrey Compère's notes on advanced topics in GR
These notes are excellent for starting PhD students in gravity and related fields, especially in holography. They cover many advanced topics which are fundamental for research:
- The covariant phase space formalism needed to fully understand conserved charges in GR.
- 3D gravity, BTZ black holes and the Chern-Simons formulation.
- Asymptotic symmetries and, in particular, asymptotically flat spacetimes and the BMS group and memory effect.
- Advanced topics about Kerr black holes like the Kerr/CFT correspondence and quasi-normal modes.
• Notes on black holes edited by Stefan Vandoren and Riccardo Borsato
I haven't personally studied much from the but they seem very complete and well done. They are very didactical and cover many special topics like black branes in AdS, no-hair theorems and perturbations of black hole geometries which are useful from astrophysics to holography.