Particles with fractional statistics interpolating between bosons and fermions have attracted the considerable interest of mathematical physicists. In recent years it has emerged that these so-called anyons have rather unexpected applications in condensed matter physics, such as the fractional Hall effect, anyonic excitations in films of liquid helium, and high-temperature superconductivity. Furthermore, they are discussed also in the context of conformal field theories. This book is a systematic and pedagogical introduction that considers the subject of anyons from many different points of view. In particular, the author presents the relation of anyons to braid groups and Chern-Simons field theory and devotes three chapters to physical applications. The book addresses researchers as well as advanced students of mathematics and physics.