What is quantum mechanics? The laws of Newton, which work well over a wide range of scale, from planets to billiard balls, fail at the level of atoms and their constituents. Quantum mechanics provides a new set of laws and a mode of description for microscopic systems that has proved supremely successful. Since its inception in the 1920s it has explained the structure of atoms and molecules, nuclear reactions, collisions of particles in accelerators, the emission and absorption of radiation, the thermal and electrical properties of solids, chemical bonding, superconductivity and superfiuidity, the pressure inside collapsed stars, subnuclear matter, and a great deal else. Why is quantum mechanics so important? Besides providing explanations for a wide variety of physical phenomena, the theory has led to a large number of practical applications, among which are the laser, the electron microscope and the microchips of modern electronics. In many research laboratories and high technology industries, devices based on quantum principles are used or developed as a matter of routine. Although the foundations of the subject are well over half a century old, new applications of the theory still have the power to surprise. Why is it so hard to learn? Students find quantum mechanics tough going for two reasons, one conceptual, the other technical. Familiar concepts such as speed, size, acceleration, momentum and energy take on weird features, or even become meaningless. Intuition gained from daily experience is of no help, and can be misleading.