Daras said:
Hi.
I want to learn - amateurishly - Quantum Mechanics, and General Relativity, but my experience with Physics is very small.
I want to ask, what should I learn - what books should I read - before I start to learn those theories?
Sorry for my english.
Quantum Mechanics requires linear algebra, abstract algebra and mathematical analysis (real and complex), so that you can study everything with full rigor. Calculus is also a requirement. It is not a sufficient but definitely necessary condition. If you want less rigor, maybe linear and abstract algebra, and introductory analysis will be enough.
Have a look at the following PF insights blogs:
Self-Studying linear algebra
Self studying abstract algebra
From physics, you need to know special relativity.
Take a look at Griffiths' book on Quantum. Chapter 3 has a lot of mathematical insights that might help you.
I would suggest lecture courses in addition to books.
For linear algebra, you can have a look at
Introduction to Abstract and Linear Algebra by Prof. Sourav Mukopadhyay. All lectures have not been released as of today, but they will soon be released. It's a good course, and the prof. teaches well. Every week, five lectures are released.
Other than that, you can refer to Prof. Balakrishnan's lectures
Quantum Physics. Though you are supposed to know linear Algebra before starting, he summaries some concepts in the first few lectures. Also, some concepts of classical mechanics would be necessary too, though not very essential.
For special theory of relativity, look at
this course by Prof. Shiva Prasad.