One of our goals in writing this book is to give the reader a simple presentation of the theory of the functions of one complex variable with a minimum of dependence and with an important number of exercises and problems with solutions to deepen the knowledge. There are three categories of exercises throughout the book. An important number of them are mainly direct applications of course results, and others are more complicated to solve. The other named problems usually require some effort to solve. A detailed solution is given for all exercises in the book.