Exact solutions in gravity and cosmology with extra dimensions

New challenges to theoretical physics and the role of gravity and cosmology are discussed. Problems of gravitation as the fundamental interaction are also analyzed. Results of integrable gravitational and cosmological models with extra dimensions with scalar fields, forms and other matter sources are presented. Their role in solving basic problems of modern cosmology and black hole physics, such as the present acceleration of the Universe, nonsingular initial state, stability of fundamental constants etc. is pointed out. © Rencontres du Vietnam All rights reserved.