Operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis.

In the present book, eight typical literatures about operator theory published on international authoritative journals were selected to introduce the worldwide newest progress, which contains reviews or original researches on operator theory. We hope this book can demonstrate advances in operator theory as well as give references to the researchers, students and other related people.