Algebraic combinatorics is the study of combinatorial objects, like graphs, designs, codes, etc., using algebraic methods. The symmetry of such an object is captured by its automorphism group, which usually can be viewed as a permutation group, and thus much of the group theory discussed above can be applied in the study of combinatorial objects which satisfy symmetry conditions. Examples of such conditions are: vertex-transitivity of a graph; flag-transitivity of a design; smooth approximation of an omega-categorical structure (these occur naturally in model theory), and so on.