Lattice paths and generalized Rogers-Ramanujan type identities

The Rogers-Ramanujan identities and their many generalizations are well known in q-series. In this thesis we will use combinatorial methods, specifically lattice paths, to give new proofs of known Rogers-Ramanujan type identities and to prove two new theorems. These theorems will allow us to derive several new polynomial identities that give new Rogers-Ramanujan identities. We will also exploit new applications of Bailey's lemma to obtain new generalizations of multisum Rogers-Ramanujan type identities.