Transfer systems are combinatorial objects that one can associate to a given finite group or a given finite lattice. they are the central objects of an emerging field called `homotopical combinatorics'. This field involves three, a priori unrelated, areas: model structures in the sense of Quillen, a family of operads coming from G-equivariant topology and the classical combinatorics of binary trees.
In this talk, we will see how one can classify the transfer systems associated with a cyclic p-group. On the other hand, we will see that it will be very hard to obtain a full classification for more general groups. This will be obtained by studying the properties of a partial ordering on the transfer systems. | 
