This volume comprises the lectures on some problems of relativistic astrophysics and cosmology delivered at the Sir Arthur Eddington Centenary Symposium celebrated at Nagpur (India). It begins with a review lecture given by Dallaporta on the active galactic nuclei and goes on with some cosmological problems, followed by some more particular topics as conformally invariant gravitation and electromagnetism, naked singularities, critical view on equation of motion, problems on torsion, on unified theories, on the role of charge in the Kaluza theory, large number coincidences, to finish with a perturbative approach to self consistent cosmologies, an extension of Eddington ideas and Eddington's contribution to astrophysics.