Finite CI-groups and Schur rings

A Cayley graph Cay(G,S) is called a CI-graph if for every subset T
of G, if Cay(G,T) and Cay(G,S) are isomorphic, then T=f(S) for some automorphism f of G. The group G is called a DCI-group if every Cayley graph of G is a CI-graph, and it is called a CI-group if every undirected Cayley graph of G is a CI-graph. Although there is a restrictive list of potentional CI-groups (Li-Lu-Pálfy, 2007), only a few classes of groups have been proved to be indeed CI; in several cases the proof was obtained by studying the Schur rings over the given group.  In my talk I will review the Schur ring method.