Classification of flag-transitive symmetric designs

A symmetric design is one which has as many points as it has blocks. There are many necessary conditions for existence of designs, but these are not sufficient. One way to attack the problem of classifying incidence structures is via the action of their automorphism groups, which permits the use of heavy group theory machinery.Here we present some results obtained in the path towards the classification of flag-transitive (v,k,λ)-symmetric designs via their automorphism groups. We start with λ=1 and 2, and move on to the still open problem of obtaining general results for any λ>2.