Determinantal point processes arise in a wide range of problems in asymptotic combinatorics, representation theory and mathematical physics, especially the theory of random matrices. While our understanding of determinantal point processes has greatly advanced in the last 20 years, many open problems remain. The course will give an elementary introduction to determinantal point processes, starting from the basics and leading on to open problems. PROGRAMME. 1. Examples. 2. Limit theorems. 3. Palm-Khintchine theory. Quasi-symmetries. 4. Determinantal point processes and extrapolation.