This talk will be a light introduction to Hochschild cohomology and algebraic deformations. I will present a cochain complex for computing the Hochschild cohomology groups for a given k-algebra. In low degrees, these groups carry information about the algebraic deformations of a given algebra. We will define what we mean by "algebraic deformation", and we explore how we may use Hochschild cohomology as a starting point for building deformations.