The aim of this book is to give an elementary and essential introduction to the stochastic integration with respect to a semi-martingale. basically the reader is supposed to be familiar with the language of probability and with the basilar notions of measure theory.

The aim of this book is to give an elementary and essential introduction to the stochastic integration with respect to a semi-martingale. It is supposed to be useful to the beginner as a starting point for additional studies and readings in the subject. The exposed theory is only about real-valued processes. The prerequisites for this book are of an average level; basically the reader is supposed to be familiar with the language of probability and with the basilar notions of measure theory.