This book deals with the Mathematica system of computer algebra, or, more generally, with that part of mathematics in which the Mathematica software can be used as a helpful tool. After introducing basic concepts of the philosophy of Mathematica’s syntax, the reader is led through the questions of data and file structures, the concept of Mathematica’s notebook, add-on packages, palettes and the general questions of establishing a communication between the user and the program. Then the basic computation (calculus) and graphics examples are given and the more sophisticated issues are discussed, such as differential equations, integral transforms and special functions. Due to the large command structure and tricky syntax, Mathematica is often considered as a computer system difficult to learn in a reasonable time. The first look at this book seems to bear out this impression; while being written for beginners, it runs to almost 700 pages, which can discourage the beginner from learning such a piece of software. On the other hand, if someone decides to learn Mathematica, books of this kind are necessary. In this book, the reader is taught step-by-step the basic skills needed to use Mathematica in practice. A “non-threatening” style of instruction is used, namely teaching by examples and practical applications. A large index list is also useful.