 This formalism is enormously successful in that correct predictions can be derived for a vast class of systems. But the success of this formalism is rather puzzling. The first and most obvious question concerns the relation of systems and ensembles. The probability distribution in the Gibbs approach is defined over an ensemble, the formalism provides ensemble averages, and equilibrium is regarded as a property of an ensemble. But what we are really interested in is the behaviour of a single system! What could the properties of an ensemble—a fictional entity consisting of infinitely many mental copies of the real system—tell us about the one real system on the laboratory table? And more specifically, why do averages over an ensemble coincide with the values found in measurements performed on an actual physical system in equilibrium? There is no obvious reason why this should be so, and it turns out that ergodicity plays a central role in answering these questions.