## Bu-Ali Sina University

A symmetric design (v,k,lambda) is an incidence structure consisting of a set of v points and a set of v blocks with an incidence relation such that every block is incident with exactly k points, and every pair of points is incident with exactly lambda blocks. An automorphism group of a symmetric design is a group of permutations on points of the design which maps blocks to blocks and preserves incidence and non-incidence. An automorphism group of a design naturally acts on the elements of the design, namely, points, blocks and flags. The main part of this talk is devoted to giving a survey on recent study of symmetric designs which admit a group of automorphism acting primitively (resp. transitively) on the set of points (resp. blocks). We in addition give a list of possible parameters of designs admitting a flag-transitive and point-primitive almost simple automorphism group with socle a finite exceptional simple group.