The business of homological algebra is to ascribe a homology theory to algebraic objects, including those that may not initially be amenable to such a theory. For instance, one may ascribe a homology theory to a module, which is a generalization of a vector space. This book does not assume familiarity with module theory, but one can still explore the beginnings of the theory by instead studying sequences of sequences. Sequences of sequences are strictly richer than sequences of vector spaces but provide enough concrete structure to reveal the outlines of the general theory. To study a given module homologically, one starts by constructing resolutions, which are exact sequences that either start or end at the given module of interest. The book ends by using these resolutions to understand homology in this generalized setting, exploring the notion of the derived category and derived functors.