This preliminary chapter is divided into two main sections. The first section presents some basic facts about Banach algebras, especially the Gelfand representation of commutative \(C^{*}\) -algebras with identity. After basic notions and notation that must be familiar to the reader, we exhibit what is justifiably considered as the corner-stone of the theory of homogenization algebras, namely the commutative Gelfand-Naimark representation theorem. Attention is focused on a few examples of those Banach algebras that underly the concept of a homogenization algebra, that is, on commutative \(C^{*}\) -algebras with identity. Finally, we conclude the section by discussing the Gelfand representation of the closed product of a finite family of \(C^{*}\) -algebras of continuous complex functions. We show that the Cartesian product of the spectra of such \(C^{*}\) -algebras is homeomorphic to the spectrum of the said closed product. The result thus established will play a crucial role in applications, especially in the study of evolution equations and in reiterated homogenization, all that in the deterministic setting.