I wanted to learn stochastic volatility modelling and interest rate modelling.
On this site, a answer recommended me the books "Stochastic Volatilty Modelling" by Lorenzo Bergmo and "Interest Rate Modelling" - a 3 volume set by Piterbarg and Andersen.
Maybe it should've been obvious, but now that I've started reading them, it is more than clear that these are not textbooks for students. Lorenzo Bergomi's book is more of an essay on stochastic volatility modelling -- a "lessons learned" type of book -- while the 3-volume book by Piterbarg and Andersen is more of a reference for modern interest rate modelling aimed at practitioners that they can can have on their shelves.
It is not so that the theoretical level is too hard: I understand everything perfectly well. I just don't think they are optimal for a student. I am looking for textbooks that place importance on the core material. When reading Lorenzo Bergomi's book for example, I have no clue what is important and what isn't, since everything is just kind of cluttered together, and he rambles (I say this respectfully) in all kinds of random directions on a whim.
Having a background in mathematics, I would much rather prefer a book with a simple structure that follows the typical Definition -> Theorem -> Lemma -> Theorem -> Example type structure, which clearly outlines what's going on and why.
So with that in mind, what are some good TEXTBOOKS aimed at students for the two topics mentioned above?