The main objective of this thesis was to find the full automorphism groups of finite Desarguesian planes. A set of homologies were used to generate the automorphism group when the order of the plane was prime. When the order was a prime power Pa,a ≠ 1 the Frobenius automorphism was added to the set of homologies, and then the full automorphism group was generated. The Frobenius automorphism was found by using the planar ternary ring derived from a coordinatization of the plane. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2013.