This chapter presents an approach for the study of connected crystals such as metal-organic and covalent-organic frameworks, MOFs and COFs, based on the mathematics of topology, topological spaces, and graph theory. Two guiding questions are posed towards topology-based crystal study and design, when are two crystals “the same,” and when are crystals “predictable.” Moving away from isostructural unit cells, here, crystals are studied as abstract topological spaces from the perspective of their van der Waals volume. First, the notions of topologies as abstract sets are introduced, and then the concepts of choice of a topology, connectedness, and continuous transformations. The chapter then presents the concepts of deconstruction and decoration as homotopic transformations that access topological subspaces of crystals (underlying nets), as sets of vertices and edges (graphs) embedded in Euclidean space. Underlying nets, the fundamental object of study in reticular chemistry, are introduced as special kinds of graphs that represent the topological information of the crystal and are used to introduce the two principles of reticular chemistry. First, The Isoreticular Principle, to answer the question of similarity of crystals and identification of nets based on homeomorphisms. Second, The Minimal Transitivity Principle that gives insight on the predictability of crystals, based on the topological simplicity of natural tilings and cell-complex extensions of nets. Last, a method for producing crystal models via decoration of nets with molecular building units is described. This method shows how topology provides a foundation for the design of MOFs and COFs that can be prepared experimentally in the laboratory.