Abstract
This thesis is devoted to the study of some quantum invariants of 3-manifolds and 4-manifolds as well as their associated TQFTs and HQFTs. We establish that for all spherical category $\C$, the Turaev-Viro TQFT comes from a 1+2 dimensional HQFT which has the classifying space $B\grad$ as target space. Using the methods developed here, we give a new description of the homological Turaev-Viro invariant. Furthermore, we introduce the notion of a Picard categories which we use to link the Dijkgraff-Witten invariant to the Turaev-Viro invariant. Lastly, we construct a 4-dimensional quantum invariant and compare it to the quantum invariant defined by Crane, Kauffman and Yetter. This invariant is obtained from pairs of premodular categories which have invertible dimensions.