This is the first of two-volume book collecting selected papers from another conference in a successfully continuing series of ‘Groups St Andrews’. It covers many different directions of research, which is carried in the Theory of Groups twenty years after the classification of the finite simple groups. The volumes contain short research articles as well as accessible surveys. In particular it contains summaries of five invited lecture courses given at the conference, which are rather hidden among the alphabetically ordered papers. They include contributions of M. Conder (Group actions on graphs, maps and surfaces with maximum symmetry), P. Diaconis (An introduction to random walk on finite groups - character theory and geometry), P. Palfy (Groups and Lattices), M. du Sautoy (Zeta functions of groups and counting p-groups) and M. Vaughan-Lee (Lie methods in group theory). The book is an excellent source describing the current status in the field.