Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the research of the foundations of statistical mechanics. This generalization of the well-known Boltzmann - Gibbs theory enables the study of systems with long-range interactions, long-term memories or multi-fractal structures. This book consists of a set of self-contained lectures and includes additional contributions where some of the latest developments - ranging from astro - to biophysics - are covered. Addressing primarily graduate students and lecturers, this book will also be a useful reference for all researchers working in the field.