In this thesis, we will axiomatize the theory of a strongly minimal unar, that is, a structure A in the language L = (f) where f is a unary function. We will first classify the strongly minimal unars where f is injective and give complete axiomatizations for them. Then we will show that these theories have quantifier elimination after adding some relation symbols. Then we will topologize A and prove that this topology satisfies the Zariski axioms. Finally we will classify all the strongly minimal unars, not necessarily the injective ones, and give an axiomatization of some of the cases of the classification.