This volume contains translations of six of the original papers of Moshe Livsic on the characteristic operator function, together with a collection of contributions devoted to Moshe Livsic&s theory of the characteristic operator function and its impact on the spectral analysis of non-selfadjoint operators, a theory first introduced in the 1940s. This theory provides a framework for the spectral analysis of non-selfadjoint and non-unitary operators and has since become a cornerstone of modern operator theory. Over the past seventy-five years, Livsic&s theory has exerted a lasting influence on analysis, complex analysis, linear systems theory, and a broad range of related topics. The volume examines how Livsic&s theory has shaped the study of pairs of commuting operators, a research direction initiated in the early 1970s with the aim of linking systems theory, non-selfadjoint operator theory, and Riemannian geometry. The contributions collected here reflect the scope and depth of Livsic&s work at the intersection of operator theory, geometry, and systems theory. This book will be a valuable resource for researchers and advanced graduate students working in operator theory, analysis, systems theory and related areas.  A number of recollections from colleagues, students and friends of Moshe Livsic are also included.