The present book "Some Hydrodynamic and Hydromagnetic Unsteady Flows " is devoted to the mathematical investigations of two- and three-dimensional problems related to unsteady, free convective, hydrodynamic and magnetohydrodynamic flows through porous and non porous medium in non-rotating and rotating systems. It is hoped that the mathematical solutions obtained in this work contribute not only to a better understanding of the problems they deal with, but also find significant applications in many engineering, industrial and environment processes e.g. solar power technologies, nuclear power plants, MHD generators and accelerators in geophysics, space vehicle reentry, polymer production, food processing and manufacturing of ceramics or glassware etc.In the present work deals with the treatment of the governing equations, i.e. Firstly the equations governing the flow are formulated, Secondly they are reduced to non-dimensional form and finally their solution is obtained by perturbation technique or series expansion method etc.