While searching around for some market making-related stuff I bumped into this paper https://arxiv.org/abs/1105.3115 and thought that I'll start digging through it and its References, out of lack of better ideas. I doubt that's a particularly effective way of approaching this, so could someone give me a better list of papers to get started with? I'm particularly interested in the theory of market making strategies for stocks, but will happily read any "classical" works in the general "quant finance" area.
The field is in flux right now. Since you are at the master's level I think you should focus on more general works in mathematics. If you were my student and we were ignoring specific things such as securities analysis and accounting and focusing on the mathematics, I would recommend you begin with measure theory, real analysis, combinatorics, Bayesian analysis and decision theory (both Bayesian and Frequentist). It's important to understand that a lot of stuff used in quantitative finance lacks empirical support. Think of other categories of problems such as the difference between two means.
Depending on your precise assumptions there are only a few possible tools and only two or three should be operative at a time, one Bayesian, one Frequentist and one Likelihoodist if it differs from the Frequentist. Once you have selected your interpretation of probability, there should only be one choice open to you.
In quantitative finance, there are tons of tools and each one is being proposed because it is not clear what to use. Tools range from OLS to GARCH, to fractal based analysis, neural networks to data envelope analysis to random forests and you can get a long list in the literature. In just one category I did a review on I found 26 techniques.
You want to stay out of the weeds AND stay out of most of the foundational documents. To understand why you need to stay out of the weeds consider that GARCH is big right now, but in the very first GARCH article they ran a test on stocks and found that stocks strongly violated the assumptions necessary for GARCH to work. Even though it is not supportable, neither are most things, so why not use it?
Go to one of your advisors or to a librarian in your academic library and start with a book on measure theory. I am not going to recommend one, but instead, suggest you talk to people about it where you are at. There is an advantage to face-to-face conversation. Then pick up real analysis. You can flip the order. As you start getting into this you will find that many of these problems are really combinatoric problems. Lots of the solutions really attempt to go around the combinatoric issues. Then I would pick up an introductory book on Bayesian methods and an introductory book on decision theory.
As you get into the field you will find someone needs you to evaluate a neural network or an ARMA model. I recommend the physicians' command "first do no harm." You are an expert in the math and not in finance or economics. Listen to them, dig deep into what they are really needing from you and what their goals are. Be as good as you can at the base math, then build into finance later.
PS It wouldn't hurt you to pick up an accounting textbook either.
I would consider "Aspect of Mathematical Finance" as a starting point for a "general quant finance area". It is
A collection of essays written by leading experts in the field of finance mathematics
For "market making-related stuff" I would try "Market Microstructure in Practice"