This book is an introduction into a new and fast developing field on the crossroads of infinite-dimensional Lie algebra theory, conformal field theory, and the theory of integrable systems. For beginners, it provides a short way to join in the investigations in these fields. For experts, it sums up the recent advances in the theory of almost graded infinite-dimensional Lie algebras and their applications. The majority of results is presented for the first time in the form of a monograph.