This book collects important results concerning the classification and properties of nilpotent orbits in a Lie algebra. It develops the Dynkin-Kostant and Bala-Carter classifications of complex nilpotent orbits and derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits.

The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary.