The aim of this summer school is to bring together and educate international PhD students and young post-doctoral fellows from physics, mathematics and engineering. Statistical methods and in particular randomness play an important role in many modern applications in physics and other natural sciences, as well as in several branches of mathematics. One of the common themes that interlaces fields as divers as probability theory, complex analysis and combinatorics is that of random matrices. On the physics side applications include the transition from classical to quantum chaos, classical problems such as random walks or the theory of spin glasses up to recent problems of entanglement in quantum computation. Random matrices also appear in optimisation in telecommunication, a very active field in engineering. The proposed school will try to cover all these topics in an intense two week summer course consisting of eight interdisciplinary, interactive lecture series led by world leading international experts.