Manifolds are generalizations of curves and surfaces, locally modelled on the Euclidean space. The tools of manifold theory are indispensable in most major sub fields of pure mathematics and are becoming increasingly important in such diverse fields as theoretical physics, robotics, computer graphics, genetics, etc. Lie groups are smooth manifolds that are also groups in which multiplication and inversion are smooth maps. They are essential tools in the study of manifolds. In this talk, we will look at the basic definitions and examples of smooth manifolds and Lie groups, and see a few examples of smooth action of Lie groups on smooth manifolds.