Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's 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 basic integration methods are derived from Lie group theory∗ Includes a concise and self contained introduction to differential equations∗ Easy to follow and comprehensive introduction to Lie group analysis∗ The methods described in this book have many applicationsThe author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.