Appears in collection : Research School in Discrete Mathematics and Computer Science / École de recherche en mathématiques discrètes et informatique - WEEK 1

In these talks, we will discuss a family of groups called diagram groups, studied extensively by Guba and Sapir and others. These depend on semigroup presentations and turn out to have many good algorithmic properties. The first lecture will be a survey of diagram groups, including several examples and gen-eralizations. The second lecture will take a geometric approach, understanding these groups through median-like geometry.