This is the first systematic presentation of the capacitory approach and symmetrization in the
context of complex analysis. The content of the book is original - the main part has not been
covered by existing textbooks and monographs. After an introduction to the theory of condenser
capacities in the plane the monotonicity of the capacity under various special transformations
(polarization Gonchar transformation averaging transformations and others) is established
followed by various types of symmetrization which are one of the main objects of the book. By
using symmetrization principles some metric properties of compact sets are obtained and some
extremal decomposition problems are solved. Moreover the classical and present facts for
univalent and multivalent meromorphic functions are proven.This book will be a valuable source
for current and future researchers in various branches of complex analysis and potential
theory.
