Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lies striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail.

• This is the first modern text on ordinary differential equations where the...