True to its title, this book is focused on mathematical finance field and it is draft in order to accomplish the level aimed at second or third year undergraduate students, not only of mathematics but also, for example, business management, finance and economics. The aim of this book is to provide the basic concepts concerning the mathematical finance which is unescapable to understand the way modern financial markets operate.Thanks to these fundamental concepts, which are completely concentrated on a deterministic modelization of the markets, students are ready to approach more advanced courses focused on the modern area of financial math. Here the deterministic assumption is left and stochastic assumptions concerning the evolution of the involved variables are included.