Publisher Summary This chapter focuses on the models of axiomatic theories based on the first order logic with identity and more specifically with automorphisms of such models. The main results of the chapter are contained in a theorem, which says that if a theory possesses at least one infinite model, it also possesses a model with a very large automorphism group. The chapter deals with theories containing an arbitrary number of constants. It presents all the notions and lemmas that are necessary to an exact formulation of the main theorems and to their proofs. It discusses the terminology and expounds the general method of constructing models for arbitrary theories. The chapter proves a theorem stating that for each group G there is a theory some models of which possess an automorphism-group isomorphic with G. It concludes that the non-constructive tools used in the proofs of principal theorems are all reducible to the fundamental theorem of the ideal theory in Boolean algebras.