The newly developed field of SeibergWitten gauge theory has become a wellestablished part of the differential topology of fourmanifolds and threemanifolds. This book offers an introduction and an uptodate review of the state of current research. The first part of the book collects some preliminary notions and then gives an introduction of SeibergWitten theory of fourdimensional manifolds. In the second part, the author introduces the dimensional reduction and uses it to describe SeibergWitten in threedimensional manifolds. In both parts, the SeibergWitten equations are derived, the moduli spaces of solutions are constructed, and the corresponding invariants of manifolds are introduced. In the third part, the author gives an overview of geometric and topological results obtained via SeibergWitten theory. Through all these parts of the book, SeibergWitten gauge theory is considered as a completely selfcontained subject and no a priori knowledge of Donaldson theory is assumed. In fact, all the sections that refer to Donaldson theory can be skipped, and this will not affect the comprehension of the remaining sections. In the final part of the book, the author describes physical theories that are responsible for the emergence of this new piece of mathematics, the SeibergWitten theory. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership Graduate students and research mathematicians interested in geometry of manifolds and gauge theory. Table of Contents  Introduction
 SeibergWitten on fourmanifolds
 SeibergWitten on threemanifolds
 Topology and geometry
 SeibergWitten and physics
 Appendix: a bibliographical guide
