This volume is dedicated to the eminent Russian mathematician I.B. Simonenko on the occasion of his 70th birthday. It presents recent results in Fredholm theory for singular integral and convolution operators, estimates for singular integral operators on Carleson curves acting in Lp spaces with variable exponents, the finite sections method for band-dominated and Toeplitz operators, Szegö type theorems, the averaging method for nonlinear equations, among others. All papers are contributed by leading experts, many of whom are connected with I.B. Simonenko as students or collaborators. The book testifies the wide mathematical interest of I.B. Simonenko and includes a biography, his list of publications and a list of his Ph.D. students.