This book is divided into two parts. The first part deals with the basics of low dimensional dynamical systems. Flows in different dimensions are considered with emphasis on non-linear oscillators as well as forced and parametrcially excited ones. One dimensional maps are studied with the primary purpose of introducing the concept of chaos and the various associated measures. In the second part the focus shifts to infinite dimensional systems -  the preferred medium for describing nature. We concentrate on magnetohydrodynamics. A self contained introduction is provided assuming no prior knowledge. Considerable attention is given to linear stability analysis as well as techniques that are non-perturbative in nature. The relevance of low dimensional systems in describing infinite dimensional ones froms the underlying theme.