在本书中，作者通过大量例题，极为详尽地讲述了在独立研究规范理论时所必需的一系列原理、技术和应用，以及它在几何和拓扑学中的应用。书中包括对大多数单连通代数曲面的 Seiberg-Witten不变量的完整且自足的计算，其中仅仅使用了 Witten 的分解法。书中还给出了剖分和粘贴 Seiberg-Witten不变量的一个新方法，并通过如下例子进行讲解：连通和定理，blow-up公式，以及对Fintushel和Stern的消灭结果的证明。本书适合用作微分几何、代数拓扑、基础偏微分方程和泛函分析的参考书。
Introduction
Chapter 1.Preliminaries
1.1.Bundles, connections and characteristic classes
1.1.1.Vector bundles and connections
1.1.2.Chern-Weil theory
1.2.Basic facts about elliptic equations
1.3.Clifford algebras and Dirac operators
1.3.1.Clifford algebras and their representations
1.3.2.The Spin and Spinc groups
1.3.3.Spin and spine structures
1.3.4.Dirac operators associated to spin and spinc structures
1.4.Complex differential geometry
1.4.1.Elementary complex differential geometry
1.4.2.Cauchy-Riemann operators
1.4.3.Dirac operators on almost Khler manifolds
1.5.Fredholm theory
1.5.1.Continuous families of elliptic operators
1.5.2 Genericity results
Chapter 2.The Seiberg-Witten Invariants
2.1.Seiberg-Witten monopoles
2.1.1.The Seiberg-Witten equations
2.1.2.The functional set-up
2.2.The structure of the Seiberg-Witten moduli spaces
2.2.1.The topology of the moduli spaces
2.2.2.The local structure of the moduli spaces
2.2.3.Generic smoothness
2.2.4.Orientability
2.3.The structure of the Seiberg-Witten invariants
2.3.1.The universal line bundle
2.3.2.The case b+ > 1
2.3.3.The case b+ = 1
2.3.4.Some examples
2.4.Applications
2.4.1.The Seiberg-Witten equations on cylinders
2.4.2.The Thom conjecture
2,4.3.Negative definite smooth 4-manifolds
Chapter 3.Seiberg-Witten Equations on Complex Surfaces
3.1.A short trip in complex geometry
3.1.1.Basic notions
3.1.2.Examples of complex surfaces
3.1.3.Kodaira classification of complex surfaces
3.2.Seiberg-Witten invariants of Khler surfaces
3.2.1.Seiberg-Witten equations on Kahler surfaces
3.2.2.Monopoles, vortices and divisors
3.2.3.Deformation theory
3.3.Applications
3.3.1.A nonvanishing result
3.3.2.Seiberg-Witten invariants of simply connected elliptic surfaces
3.3.3.The failure of the h-cobordism theorem in four dimensions
3.3.4.Seiberg-Witten equations on symplectic 4-manifolds
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