Lectures on mathematical finance and related topics Rigorous mathematical finance relies strongly on two additional fields: optimal stopping and stochastic analysis. This book is the first one which presents not only main results in the mathematical finance but also these related topics with all proofs and in a self contained form. The book treats both discrete and continuous time mathematical finance. Some topics such as Israeli (game) contingent claims and several proofs have not appeared before in a self contained book form. The book contains exercises with solutions at the end of it and it can be used for a yearlong advanced graduate course for mathematical students. Martingales and optimal stopping Derivatives in general and binomial markets Fundamental theorems of asset pricing Superhedging Hedging with risk Martingales in continuous time and optimal stopping Introduction to stochastic analysis Derivatives in the Black Scholes market Discrete time case Continuous time case Solutions of exercises.