This paper includes three parts:　　 PART I: A maple package to compute Lie symmetry groups and the symmetry reductions of (1+1)-dimensional nonlinear systems 　　 Armed with the computer algebra system Maple, using a direct algebraic substi-tution method, Lie point symmetries, Lie symmetry groups and the corresponding symmetry reductions of one component nonlinear integrable and nonintegrable equations could be ob tained only by clicking the "Enter" key. Abundant (1+1)-dimensional nonlinear mathemat ical physical systems have been analyzed effectively by using the Maple Package LieSYMGRPproposed by us.　　 PART Ⅱ: Infinite series symmetry reduction solutions to the modified KdV-Burgers equation 　　 From the approximate symmetry point of view, a special modified KdV-Burgers　　 (mKdV-Burgers)equation with weak dissipation is investigated. The symmetry of a system of the corresponding PDEs which approximates the perturbed mKdV-Burgers equation is constructed and the corresponding general approximate symmetry reduction to the perturbed mKdV-Burgers equation is derived, which enables infinite series solutions and general for mulae.It is noticeable that the similarity solutions of zero-order satisfy Painlevè Ⅱ equation.Finally, by choosing the solitary wave solutions of the unperturbed mKdV-Burgers equation,namely, mKdV equation, as initial approximate, the physical approximate similarity soluotions are obtained step by step under appropriate choices of parameters occurred during the computations.　　 PART Ⅲ: Approximate symmetries and infinite series symmetry reduction solutions to the perturbed Kuramoto-Sivashinsky equation 　　 Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky (KS) equation. The approximate symmetry reduction and the infiniteseries symmetry reduction solutions of the perturbed KS equation are constructed. Specially,if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.