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Symmetries, Singularities and Integrability in Nonlinear Mathematical Physics and Cosmology

An overview is given of the interplay between symmetries, singularities and integrability and their uses in nonlinear problems arising in Mathematical Physics and Cosmology. A particularly important aspect is the role of nonlocal symmetries in deciding about integrability of complex nonlinear problems which do not apparently admit solutions in closed form. The need for a new approach to the evolution of symmetries themselves is also discussed.