In random matrix theory, it is believed that the local statistics of eigenvalues of a general class of random matrices are universal in the sense that they do not depend on the distribution of matrix entries. The universality can be divided into two different types, the bulk universality and the edge universality, each of which concerns the probability density of eigenvalues in the interior and at the extreme edge of the spectrum, respectively. In this talk, the universality results and basic tools to study random matrices will be covered.