From Frenet to Cartan:
The Method of Moving Frames

From Frenet to Cartan: The Method of Moving Frames, Graduate Studies in Mathematics 178, American Mathematical Society (2017), 414 pp.

Available here.

Reviews:

• "An excellent and unique graduate level exposition of the differential geometry of curves, surfaces and higher-dimensional submanifolds of homogeneous spaces based on the powerful and elegant method of moving frames. The treatment is self-contained and ilustrated through a large number of examples and exercises, augmented by Maple code to assist in both concrete calculations and plotting. Highly recommended."  --Niky Kamran, McGill University

• "Cartan theory remains a touchstone in modern differential geometry, and Clelland's book provides a fine new introduction that includes both classic and contemporary geometric developments and is supplemented by Maple symbolic software routines that enable the reader to both tackle the exercises and delve further into this fascinating and important field of contemporary mathematics. Recommended for students and researchers wishing to expand their geometric horizons." --Peter Olver, University of Minnesota