It is a great pleasure for me to write this introduction to the volume celebrating Graeme Segal's 60th birthday. Graeme was one of my first Ph.D. students but he rapidly moved on to become a collaborator and colleague. Over the years we have written a number of joint papers, but the publications are merely the tidemarks of innumerable discussions. My own work has been subtly influenced by Graeme's point of view: teacher and student can and do interchange roles, each educating the other.

Graeme has a very distinctive style. For him brevity is indeed the soul of wit, arguments should be elegant and transparent, lengthy calculations are a sign of failure and algebra should be kept firmly in its place. He only publishes when he is ready, when he is satisfied with the final product. At times this perfectionist approach means that his ideas, which he generously publicizes, get absorbed and regurgitated by others in incomplete form. But his influence is widely recognized, even when the actual publication is long-delayed.

Topology has always been at the heart of Graeme's interests, but he has interpreted this broadly and found fruitful pastures as far away as theoretical physics. There was a time when such deviation from the strict path of pure topology was deemed a misdemeanour, particularly when the field into which Graeme deviated was seen as less than totally rigorous.