This book presents a step-by-step guide to the basic theory of multivectors and spinors with a
focus on conveying to the reader the geometric understanding of these abstract objects.
Following in the footsteps of M. Riesz and L. Ahlfors the book also explains how Clifford
algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary
dimensions.The book carefully develops the basic calculus of multivector fields and
differential forms and highlights novelties in the treatment of e.g. pullbacks and Stokes's
theorem as compared to standard literature. It touches on recent research areas in analysis and
explains how the function spaces of multivector fields are split into complementary subspaces
by the natural first-order differential operators e.g. Hodge splittings and Hardy splittings.
Much of the analysis is done on bounded domains in Euclidean space with a focus on analysis at
the boundary. The book also includes a derivation of new Dirac integral equations for solving
Maxwell scattering problems which hold promise for future numerical applications. The last
section presents down-to-earth proofs of index theorems for Dirac operators on compact
manifolds one of the most celebrated achievements of 20th-century mathematics.The book is
primarily intended for graduate and PhD students of mathematics. It is also recommended for
more advanced undergraduate students as well as researchers in mathematics interested in an
introduction to geometric analysis.
