Abstract In this chapter we begin the detailed structure of anyon theories, or TQFTs. We introduce the concept of fusion and explain how it is related to the Hilbert space of the anyon systems. We emphasize the importance of locality as a principle for understanding anyons. Associativity is a strong constraint on possible particle fusion rules. As examples, we introduce both Fibonacci anyons and Ising anyons. We explain how the fusion rules of an anyon theory can be used to calculate the degeneracy of the ground state on arbitrary 2-manifolds.