Cartan for beginners : differential geometry via moving frames and exterior differential systems

"This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior, differential systems and the method of moving frames. The book presents thorough and modern treatments of both subjects, including their applications to classic and contemporary problems." "The book begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples le...