Singularities of a variety may be resolved by birational transformations. This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic.

Based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, this book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, ...

This volume is designed for students and teachers who love mathematics, and can expand on local school curriculum subjects. This first volume addresses various topics in number theory.