 It turns out that ergodicity is only the bottom level of an entire hierarchy of dynamical properties. This hierarchy is called the ergodic hierarchy, and the study of this hierarchy is the core task of a mathematical discipline called ergodic theory. This choice of terminology is somewhat misleading, since ergodicity is only the bottom level of this hierarchy and so EH contains much more than ergodicity and the scope of ergodic theory stretches far beyond ergodicty. Ergodic theory (thus understood) is part of dynamical systems theory, which studies a wider class of dynamical systems than ergodic theory. 