This volume, which is dedicated to Yuri Karlovich on the occasion of his 75th birthday, includes biographical material, personal reminiscences, and carefully selected papers. The contributions constituting the core of this volume are written by mathematicians who have collaborated with Yuri or have been influenced by his vast mathematical work. They are devoted to topics of Yuri Karlovich's work for five decades, starting with his work on singular integral operators with shift, then broadened to include Toeplitz, Wiener-Hopf, Fourier and Mellin convolution and pseudodifferential operators, factorisation of almost periodic matrix functions, and local trajectory methods for the study of algebras of convolution and singular integral operators.