The importance of the nonlinear systems due to their common occurrence in the study of physical phenomena and also the various limitations posed by the linear systems theory have been the prime reasons for the studies of nonlinear models as such. The physical situations in which nonlinear equations arise tend to be highly idealized with the assumption of constant coefficients. Due to this, much attention has been paid on study of nonlinear equations with variable coefficients. This book deals with nonlinear partial differential equations with variable coefficients representing some interesting physical systems viz. coupled KdV system, generalized Hirota-Satsuma KdV, variant Boussinesq, modified Boussinesq and a family of non-evolution equations, from the view point of their underlying Lie point symmetries and to obtain their exact solutions. Since the nonlinear systems with variable coefficients are very difficult to handle, hence this book shall provide freedom for the researchers to obtain the symmetries and exact solutions for variable coefficients nonlinear systems and further to simulate the desired physical situations.