This course on quantum mechanics offers a fresh and modern approach to the field. It is a textbook on the principles of the theory, its mathematical framework and its first applications. It consistently refers to modern and practical developments, such as tunneling microscopy, quantum information, Bell inequalities, quantum cryptography, Bose-Einstein condensation and quantum astrophysics. The book contains 92 exercises with their solutions. Supplementary material on extras.springer.com contains outstanding and "easy access" Java-based simulations, which illustratively help the user to better understand how the theory actually operates. It also contains a variety of links where one can discover updated applications and further readings. A complementary book The Quantum Mechanics Solver guides students to applying the theory developed here to research problems in atomic and molecular physics, condensed matter and laser physics.