This book reflects on methods of determining the exact solutions for the velocity and shear stress corresponding to motion of Oldroyd-B and second grade fluids in different geometric scenarios. Retarded and advanced quantum Green's functions have also been used to derive new forms of kadanoff-Baym equations for a system of interacting particles in Quantum Statistical Mechanics to analyze the question to what extent Landau-Silin kinetic equations for Neutral Fermi liquid take into account quickly varying disturbances. This book introduces new results in the area of fluid dynamics and Quantum Fermi liquids.