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Harmonic maps between Riemannian manifolds were first established in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

Harmonic maps. --- Integral equations. --- Yang-Mills theory. --- Harmonic maps --- Yang-Mills theory --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Geometry, Differential. --- Differential geometry --- Maps, Harmonic --- Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Partial differential equations. --- Functions of complex variables. --- Differential geometry. --- Calculus of variations. --- Global Analysis and Analysis on Manifolds. --- Differential Geometry. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Several Complex Variables and Analytic Spaces. --- Mappings (Mathematics) --- Global analysis. --- Global differential geometry. --- Differential equations, partial. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Partial differential equations --- Geometry, Differential --- Complex variables --- Elliptic functions --- Functions of real variables --- Isoperimetrical problems --- Variations, Calculus of --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic