A gentle introduction to homological mirror symmetry This book grew out of an advanced masters course that I teach biannually at the University of Amsterdam. The course is aimed at students who are doing a masters in algebra and geometry or mathematical physics. In this course I try to give them the feeling of what homological mirror symmetry is and how it ties together many different areas of mathematics. The focus of the course is to explain the main concepts and results and to illustrate them with examples without getting too technical. In this way the students will be better prepared to delve into the primary literature if they want to understand the theory at a deeper and more detailed level