This book is devoted to an exposition of the theory of polynomially convex sets.Acompact N subset of C is polynomially convex if it is de?ned by a family, ?nite or in?nite, of polynomial inequalities. These sets play an important role in the theory of functions of several complex variables, especially in questions concerning approximation. On the one hand, the present volume is a study of polynomial convexity per se, on the other, it studies the application of polynomial convexity to other parts of complex analysis, especially to approximation theory and the theory of varieties. N Not every...