The main goal of this Précis is to mitigate the insufficiency of the traditional financial mathematics books, which don’t give enough credit to the last advances in Finance regarding the modern methods of financial valuation of assets, the analysis of new instruments, and the analysis of the risk. From what we know to what we expect from the future, this book introduces the mathematics related to the new financial instruments placing greater emphasis on new methods without sacrificing traditional financial mathematics. The first part focuses on interest rates, financing methods, and investments. And, the second part, more complex in its mathematical formalization, analyzes the instruments of interest rates both in the short and in the long term, the stocks and the portfolio theory, the options, and other conditional instruments.