This talk reviews the modern formulation of the basic ideas of quantum mechanics. We start by explaining what quantum amplitudes are, how they lead to the idea of a quantum state and how these states evolve in time. We then discuss what happens when a measurement is made before describing correlated ('entangled') systems. Applying these ideas to two-state systems ('qubits') we point out that the complexity of computing the evolution of an N qubit system grows like exp(N)