This course gives an introduction to random matrix theory (RMT), which has become a very important tool in communication systems, signal processing and a wealth of (high dimensional) statistical applications. Topics include: introduction to RMT models in engineering; eigenvalue distributions; Wishart and related distributions; finite-dimensional and large-dimensional techniques. Applications include wireless communications, array processing, robust covariance estimation, principal component analysis, signal detection, data analysis applications to financial and biomedical engineering.