In 2018/2019 we will focus on a new monograph by Cherlin, in particular on the chapter on classification of metrically homogeneous graphs.
A structure is homogeneous if every partial isomorphism extends to an automorphism.
For example, every homogeneous graph is thus also edge and vertex transitive.
It is intuitively clear that such extremely symmetric structures are rare.
The classification programme of homogeneous structures is a project of giving complete catalogs of homogeneous structures of given type (graphs, digraphs, metric spaces etc.)