  The random matrix ensembles are applied to the quantum chaotic systems. The
quantum systems are studied using the finite dimensional real, complex and
quaternion Hilbert spaces of the eigenfunctions. The linear operators
describing the systems act on these Hilbert spaces and they are treated as
random matrices in generic bases of the eigenfunctions. The random
eigenproblems are presented and solved. Examples of random operators are
presented with connection to physical problems.
