Abstract We introduce the idea of the path integral and use it to study the properties of identical particles under exhange. We explain why the topology of paths through space-time, the fundamental group of the configuration space (the braid group in 2+1 dimensions and the permutation group in 3+1 dimensions) determines the possible particle types. We argue that in 3+1 dimensions one only has bosons and fermions but in 2+1 dimensions other particles, known as anyons, can exist. We describe both the abelian and nonabelian type of anyon and argue why nonabelian anyons could be useful for quantum computation. We introduce the notion of the “quantum dimension” of an anyon which describes the size of the many anyon Hilbert space.