In this thesis, we give at first a short history of nets, some related concepts and fundamental theorems. The nets which are combinational geometric structures, were suggested at first by Walter Blashke in 1928. Considerable development have been achieved in recent decades by professor Helmut Karzel and his colleague in this theory. An important aim in studying these structures is They found a then we could · Karzel restricted chain structures to symmetric and double symmetric chain structures, for studying sharply 1,2 and 3-transitive permutation groups more accurately. We will discuss about these structures precisely in the second chapter of this thesis. Then affine plane and K-loops will be expressed after definition and pre-requirement used in third and fourth chapters including incidence structures. In the third chapter we recall at first automorphism groups of chain structures. Then we generalize these definitions to double symmetric chain structures. Subsequently, fundamental theorems about the action of these groups on double symmetric chain structures will be discussed. In the last section, we define automorphism groups of symmetric chain structures. In the fourth chapter of this thesis, we give some examples of 1,2 and 3-double symmetric structures which are webs, double symmetric 2-structures and double symmetric Minkowskie planes respectively. Then theorems mentional in second chapter will be applied on these structures. Then we investigate symmetric nets. In the last section of this chapter, point symmetric 2-structures and the relation between these structures and K-loops will be discussed.