This thesis begins with a brief introduction of Einstein’s general theory of relativity, and the applications of this theory to modern cosmology. We will, in this application, go through some classical, spatially homogeneous and isotropic cosmological models of our Universe based on Freidmann-Robertson-Walker line element. Further, we introduce the statefinder formalism, and we apply this formalism to some classical and viscous fluid universe models. We rederivesome well-known results, but, we also find new results for some of models. Following this introduction we investigate viscous fluid cosmological models of Bianchi Type-I with shear, bulk and nonlinear viscosity. Our primary goal is to analyze these viscous universe models by means of statefinder formalism.