We review the basic notions of the Random Matrix Theory and in particular the Gaussian Unitary Ensemble. In what follows we describe the Dyson gas in equilibrium and nonequilibrium that allows one to interpret the statistical information of the eigenvalues of random matrices. Furthermore we show alternative descriptions of this statistical information. In the following we discuss different aspects of orthogonal polynomials. One of these caracterizations is given by a Riemann Hilbert problem. Riemann Hilbert problem techniques are an efficient and powerfull tool for Random Matrix Theory which we discuss in more detail. In the final part we use the steepest descent method in the asymptotic analysis of orthogonal polynomials.