The quantum mechanics of systems for which the corresponding classical system can exhibit chaos. This subject was initiated by Einstein in 1917, who showed that the quantization conditions associated with the Bohr theory need to be modified for systems that show chaos in classical mechanics. The subject of quantum chaos is an active field of research in which many basic issues still require clarification. It appears that systems exhibiting chaos in classical mechanics do not necessarily exhibit chaos in quantum mechanics. In quantum mechanics, chaos can be investigated in terms of randomness, either of the evolution in time of the Schrödinger equation or its eigenfunctions and eigenvalues.