Categorification of representations of quantum groups and invariants of tangle cobordisms

In this dissertation we construct an extension of the are ring Hn and use it to cate-gorify the action of tangles on tensor powers of fundamental representation of Uq (sl2). Next, we give a more general extension and show that it leads to a categorification of level two representations of Uq(slN). These rings also induce invariants of tangle cobordisms.