The book "Mathematical Methods of Quantum Optics" offers a systematic and comprehensive presentation of the mathematical methods in quantum optics. It is particularly aimed at researchers who are new to this field and emphasizes a clear, independent, and concise presentation of the content. The authors have set out to provide a unified understanding of the concepts and methods of quantum optics to prepare readers for specific applications. The book brings together a variety of formulas that are scattered throughout the scientific literature in a logical and comprehensible manner. The structure of the book first introduces the fundamental physical and mathematical concepts before applying them to the construction of the model Hamiltonians of atom-field interaction and the master equation for systems interacting with their environment. The analysis of the resulting equations is also addressed.