This chapter presents mathematical concepts from category theory, which constitute the basis for the results discussed in the upcoming chapters. We start with the introduction of basic ideas of category theory and related definitions. After that, constructions on categories and abstract structures are defined. Next, lattice of theories concept is also important for some parts of this book, therefore it will be introduced in this chapter as well. After that, this chapter presents categorical ontology logs, or simply ologs, which combine flexibility of classical all-purpose ontologies and mathematical rigorosity of category theory. Finally, we discuss some classical and more recent applications of category theory focusing in particular on applications related to conceptual modelling.