This work is presented as a compilation of simplified literature intended to make random matrix theory accessible to anyone with a basic knowledge of quantum mechanics. The text focuses on the classical Gaussian ensembles, which consist of random matrices that, from a physical perspective, can be understood as collections of Hamiltonians whose matrix elements are random variables following a normal distribution with zero mean. In particular, their eigenvalues do not represent the energies of a specific physical system, but rather provide a global statistical description that may be shared by different systems. This is because the classification of the ensembles depends on the general symmetries of the Hamiltonians. As a result, their probability distribution depends on a factor $\beta$, which takes a different value for each ensemble.

Nevertheless, for a very large number of eigenvalues, all these ensembles exhibit the same behavior, as if they were modeling a single physical system, since their spectral density converges to the same equilibrium distribution, corresponding to the minimum of the Coulomb-gas energy functional.