This book introduces the foundational concepts and practical applications of nonstandard analysis. It is written for mathematicians and advanced students seeking to understand this rigorous framework for calculus, which allows for the formal manipulation of infinitesimals and infinite numbers. The text builds upon standard real analysis but introduces the hyperreal number system as a tool for simplifying proofs and developing new mathematical insights.

As part of the Lecture Notes in Mathematics series, this book is positioned as a rigorous academic text. Its focus on practical applications suggests it aims to bridge theoretical understanding with problem-solving utility for mathematicians and advanced students. The subject matter indicates a dense, technical treatment of calculus, likely appealing to specialists in mathematical analysis or those interested in foundational mathematics.