Preinvex Functions and Integral Inequalities In this thesis, preinvex functions and their variant forms have been considered and inves- tigated. Hermite-Hadamard type inequalities are obtained for Godunova-Levin type and h-preinvex functions. New classes of geometrically preinvex functions are introduced. Var- ious new integral inequalities for the geometrically preinvex functions are derived. Some special cases are discussed, which can be obtained from our main results. Results obtained in this thesis can be viewed as an important and signi¯cant re¯nement of the previously known results