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The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern--Weil construction in infinite dimensions, the Hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics.

Infinite-dimensional manifolds. --- Infinite dimensional Lie algebras. --- Differential equations, Partial. --- Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Lie algebras --- Manifolds, Infinite-dimensional --- Global analysis (Mathematics) --- Topological manifolds --- Partial differential equations

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Homology theory --- Noncommutative differential geometry --- 512.73 --- Differential geometry, Noncommutative --- Geometry, Noncommutative differential --- Non-commutative differential geometry --- Infinite-dimensional manifolds --- Operator algebras --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- 512.73 Cohomology theory of algebraic varieties and schemes --- Cohomology theory of algebraic varieties and schemes