Deals with continuous groups with applications to various topics in geometry and algebra. This work makes free use of geometrical ideas both in the illustrative examples and in the proofs, so that the underlying geometrical motivations are made clear.

Sophus Lie had a tremendous impact in several areas of mathematics. His work centered on understanding continuous transformation groups and showing how these groups supply an organizing principle for different areas of mathematics. This book discusses Lie's classification of all three-dimensional groups and their possible actions on the plane.