Symmetries of differential equations, deducing new solutions from unknown solutions, solution of ODE and system of ODE using Lie symmetries, Reduction of partial differential equation PDEs by reducing the number of independent variables, Linearization of ODEs by invertible transformation and exact solutions using integration strategies, computing 1st integrals/ conservation laws for differential equations and system of differential equatioins, constructing solution of ODEs and PDEs by using first integrals.
Applications of Lie Groups to Differential Equations by 
