Multidimensional gravity and cosmology and problems of G

Main trends in modern gravitation and cosmology and their relation to unified models are analysed. The role of multidimensional gravitational models with different matter sources in solving the basic problems of cosmology is stressed. Exact solutions in multidimensional cosmology with p-branes for some special cases are considered. The Riemann tensor squared is calculated in a general case and investigated for a number of special solutions. Singularities of the Riemann tensor squared are also disscussed. Also the case of static internal spaces is considered. It is shown that external space for this case is de Sitter or anti-de Sitter one. Behaviour of cosmological constant and its generation by p-branes is demonstrated.