This graduate text covers the background theory of various effects discussed from first principles, introduces students to the main ideas of quantum optics as clearly as possible, and teaches the mathematical methods and techniques used by researchers working in the fields of quantum and atom optics. The textbook contains numerous valuable derivations and calculations, hard to find in scientific articles and textbooks on quantum optics. No attempt has been made to explore all possible problems of quantum and atom optics, but it is hoped that the problems explored here will provide a useful starting point for those interested in learning more.