Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. From 1977 onwards his interest moved in the direction of gauge theories and the interaction between geometry and physics. This work deals with the gauge theories.

94. Deformations of instantons. ; 95. Instantons and algebraic geometry. ; 96. Construction of instantons. ; 97. Self-duality in four-dimensional Riemannian geometry. ; 98. Geometrical aspects of gauge theories. ; 99. Geometry of Yang-Mills fields. ; 100. Real and complex geometry in four dimensions. ; 101. Green's functions for self-dual four-manifolds. ; 102. Topological aspects of Yang-Mills fields. ; 103. Remarks on Morse theory. ; 104. Yang-Mills and bundles over algebraic curves. ; 105. The Yang-Mills equations over Riemann surfaces. ; 106. Convexity and commuting Hamiltonians. ; 107. Angular momentum, convex polyhedra and algebraic geometry. ; 108. Convexity and loop groups. ; 109. The moment map and equivariant cohomology. ; 110. The moment map in symplectic geometry. ; 111. Gauge theory and algebraic geometry. ; 112. The Yang-Mills equations and the structure of 4-manifolds. ; 113. Geometry of monopoles. ; 114. Solutions of classical equations in gauge theories: fundamental interactions and rigorous results. ; 115. Low-energy scattering of non-abelian monopoles. ; 116. Low-energy scattering of Non-Abelian magnetic monopoles. ; 117. Instantons in two and four dimensions. ; 118. Magnetic monopoles in hyperbolic space. ; 119. Anomalies and index theory. ; 120. Dirac operators coupled to vector potentials. ; 121. Topological aspects of anomalies. ; 122. Commentary on Manin's manuscript New dimensions in geometry. ; 123. Eigenvalues of the Dirac operator. ; 124. Circular symmetry and stationary-phase approximation.

'Now a single book suffices to provide not only some of the standard references and proofs, but also a variety of informal survey articles which set the whole area in context ... an essential reference.' N.J. Hitchin, Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts