Theory of Transformation Groups I

The modern translation of "Theorie der Transformationsgruppen I" reveals the conceptual clarity and systematic organization of Lie and Engel's original work. Volume I introduces the theory, focusing on generalizing ideas from various examples. It offers a clear translation alongside contemporary insights to help readers grasp key concepts. The editor aims to reignite interest in classifying Lie algebras and accessing Lie's Galois theory of continuous transformation groups. This volume is valuable for researchers in Lie theory, differential systems, and mathematics history, requiring a foundation in differential calculus and geometry.