This chapter introduces the central mysteries of quantum mechanics. Quantum mechanics is an enormously successful theory that lies at the heart of modern physics, but there is no agreement on how to understand it. Simple experiments with light demonstrate why: in understanding those experiments, we have to shift inconsistently back and forth between thinking of the theory as assigning indefinite, delocalized, but known properties to a system, and assigning definite, localized, but unknown properties (this is called the ‘problem of measurement’). Furthermore, when we break a system into subsystems, the state of the system is not determined by the states of the subsystem (this is called ‘entanglement’), and simple arguments seem to tell us that the physical properties of entangled subsystems can influence one another non-locally—faster than light. These three mysteries—measurement, entanglement, non-locality—need to be addressed by any attempt to make sense of quantum theory.