This book is a comprehensive survey of most of the theoretical and experimental achievements in the field of quantum estimation of states and operations. Albeit still quite young, this field has already been recognized as a necessary tool for research in quantum optics and quantum information, beyond being a fascinating subject on its own as it touches upon the very conceptual foundations of quantum mechanics. The books consists of twelve extensive lectures that are essentially self-contained and modular allowing to combine various chapters as a basis for advanced courses and seminars on theoretical or experimental aspects. The last two chapters, for instance, form a self-consistent exposition on quantum discrimination problems. The book will benefit graduate students and newcomers to the field as high-level but accessible textbook, lecturers in search for advanced course material and researcher wishing to consult a modern and authoritative source of reference.