This book draws a colorful and widespread picture of global affine hypersurface theory up to
the most recent state. Moreover the recent development revealed that affine differential
geometry as differential geometry in general has an exciting intersection area with other
fields of interest like partial differential equations global analysis convex geometry and
Riemann surfaces.The second edition of this monograph leads the reader from introductory
concepts to recent research. Since the publication of the first edition in 1993 there appeared
important new contributions like the solutions of two different affine Bernstein conjectures
due to Chern and Calabi respectively. Moreover a large subclass of hyperbolic affine spheres
were classified in recent years namely the locally strongly convex Blaschke hypersurfaces that
have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The
authors of this book present such results and newmethods of proof.
