I know this question has been asked several times (see: here, here, here, here, and here), but what are the "best" books on stochastic calculus: has anyone had experience with enough books on this topic so to be able to provide a unified list of books?
More specifically, assuming prior exposition to measure-theoretic probability, what is the best introduction to stochastic calculus, that is the book that keeps your hand the most while not sacrificing math rigour? The books I have in mind for this level, for example, are Kuo, Le Gall, and Oksendal.
Then, what would be the books with intermediate difficulty wrt the unanimous (?) bible Revuz-Yor (possibly listed by increasing difficulty)? The books I have in mind here are Protter and Karatzas-Shreve.