Some progress on classification problems for finite dimensional Hopf algebras has been made recently. In this thesis, we look at 4p-dimensional Hopf algebras over an algebraically closed field of characteristic zero. We show that a non-semisimple Hopf algebra of dimension 4p with an odd prime p is pointed if, and only if, this Hopf algebra contains more than two group-like elements. Moreover, we prove that non-semisimple Hopf algebras of dimensions 20, 28 and 44 are either pointed or dual-pointed, and this completes the classification of Hopf algebras of dimension 20, 28,and 44.