long story short, I am looking for good materials to help on the way to deeply understand mechanics of models

used presently to evaluate financial instruments on the market.

The long-term goal is maybe to catch-up on the latest theoretical results in the area.

I studied analysis in theory at the university, so I am primarily skilled in topics like

ODE and PDE, dynamical systems, functional analysis, measure theory.

However I don't have very much of the education on topics like advanced statistics or stochastic processes.

I had a course in probability and statistics that finished with basic types of discrete and continuous distributions,

and their parameters, and some lectures on random vectors.

From business math I am familiar only with the basics, like interest types, term structure of interest rates

and forward rates, bonds pricing, projects profitability, equations of value and stuff like that.

I'd rather build the knowledge from the basics than start from the middle,

so what I am asking is maybe to help to choose materials to cover needed topics on the way to the ultimate goal.

Thanks and regards

A.