This tutorial is aimed at anyone who wants to finally understand the physics and mathematics of quantum mechanics from the ground up: What exactly is a Hilbert space? What is a Hermitian operator? A tensor product? An entangled state? In what way are wave functions vectors? The book covers the material of the corresponding lecture course in theoretical physics in a memorable and easily understandable manner. It focuses on the general postulates of quantum mechanics and also addresses questions regarding the interpretation of quantum mechanics. Each step and each new term is explained using simple examples. The author places great emphasis on the clarity of the mathematics used—something he and many students have often found lacking in other textbooks.