This volume of the Birkhäuser “Operator Theory” series is dedicated to I. Simonenko on the occasion of his 70th birthday. The book starts with a brief description of Simonenko's life and his contributions to two important parts of his scientific work, namely to the local method for singular integral operators and the averaging method for nonlinear equations of parabolic type. The list of Simonenko's publications and his students are added. The book contains 13 papers written by colleagues and former students of I. Simonenko. These contributions are devoted to various aspects of operator theory (matrix-valued functions and their factorizations, block operator matrices and the Fredholm theory for them, Toeplitz and Hankel type operators, asymptotics of operator determinants and contraction operators), in particular to convolution operators (e.g. applications of Lévy processes in option theory) and singular operators. Three papers are closely related to the above mentioned Simonenko activity. The book will be interesting for advanced graduate students and researchers in operator theory and its applications to mathematical physics, hydrodynamics and financial mathematics.