"This book describes how to use quaternions and spinors to study conformal immersions of Riemann surfaces into R[superscript 3]. The first part develops the necessary quaternionic calculus on surfaces, its application to surface theory and the study of conformal immersions and spinor transforms. The integrability conditions for spinor transforms lead naturally to Dirac spinors and their application to conformal immersions. The second part presents a complete spinor calculus on a Riemann surface, the definition of a conformal Dirac operator, and a generalized Weierstrass representation valid for all surfaces. This theory is used to investigate first, to what extent a surface is determined by its tangent plane distribution, and second, to what extent curvature determines the shape.". "The book is geared toward graduate students and researchers interested in differential geometry and geometric analysis and their applications in computer vision and computer graphics."--BOOK JACKET.