This book is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. There exist quite a few monographs, textbooks and reviews devoted to simple (or N = 1) supersymmetry, including detailed presentations of the N = 1 superfield techniques, the natural language for N = 1 supersymmetry. However, until now there has been no systematic treatment of the analogous issues in extended (N ≥ 2) supersymmetry. In view of the growing interest in extended supersymmetries, mainly inspired by the impressive developments in superstring theory during the last decade, the need for such a presentation is becoming urgent. The present book is intended to partly fill this gap, mainly with regard to the simplest extended supersymmetry, the N = 2 one. We hope to convince the reader that the natural framework for dealing with N = 2 supersymmetry is harmonic superspace, an extension of the ordinary superspace of Salam and Strathdee by the bosonic coordinates of the supersymmetry automorphism (or R symmetry) group. The harmonic superspace approach provides a concise, manifestly covariant and off-shell description of all of the N = 2 supersymmetric theories, at both the classical and quantum levels. It also offers the unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely, the N = 3 supersymmetric Yang–Mills theory.