In this course, we will introduce some main questions and methodologies of random matrix theory (RMT), as well as the applications of RMT in physics and statistics. Since the field is huge, we will focus on a few selected topics. Our aim is to cover topics like Wigner semicircle law, Marchenko-Pastur law; Moment method; Stieltjes transform method; Gaussian ensembles and the joint distribution of eigenvalues; Orthogonal polynomial; Local statistics in the bulk: sine kernel, gap distribution; Local statistics at the edge: Airy kernel, Tracy-Widom distribution; Application in high-dimensional statistics.