Assuming foundational knowledge of special and general relativity, this book guides the reader on issues surrounding black holes, wormholes, cosmology, and extra dimensions. Its first part is devoted to local strong field configurations (black holes and wormholes) in general relativity and the most relevant of alternative theories: scalar-tensor, f(R) and multidimensional theories. The second part is on cosmology, including inflation and a unified description of the whole evolution of the universe. The third part concerns multidimensional theories of gravity and contains a number of original results obtained by the authors. Expository work is conducted for a mechanism of symmetries and fundamental constants formation, while the original approach to nonlinear multidimensional gravity that is able to construct a unique perspective describing different phenomena is highlighted. Much of the content is new in book publications, because it was previously found only in journal publications, e.g. regarding regular black holes, various scalar field solutions, wormholes and their stability, and multidimensional gravity. Readership: Students and professionals in astrophysics/cosmology.