Focusing on holomorphic curve theory within contact geometry, this book introduces the subject through a specific geometric problem. It serves as both a preparatory guide and an entry point for readers aiming to delve deeper into the analysis that supports symplectic field theory, making complex concepts accessible and engaging.
This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is to provide an entry point into symplectic field theory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in the literature in detail, top off the scope of this monograph.