This book is a solution of the so-called Einstein's Machian Program, that left Einstein very angry and frustrated, for he was unable to reconcile Relativity Theories with Ernst Mach ideas, that by looking into the Cosmos as a whole, absolute motion could be found. About one hundred years ago, the discussion led to no conclusions among physicists, so that now Berman found that the existence of a Universal rotation, was compatible with General Relativity, and that this rotation is "absolute". Berman thus solved the problem.

This book is an introduction to the General Relativity Theory (GRT) and to the solution of the Pioneers Anomaly by means of relativistic cosmology, a study that is designed to be understood by undergraduate and graduate students alike in the fields of theoretical physics, applied mathematics and space engineering. In fact, this book is the first elementary account of GRT and cosmology to address the NASA problem, which consists of a specific deceleration suffered by two space-probes launched to outer space more than thirty years ago. The other two NASA anomalies, which are, the spin-down of the Pioneers, when they were not disturbed, and the "fly-by" of spacecraft in gravity assists, around the Earth, are explained by Berman, along with the linear deceleration, by the rotation of the Universe, and General Relativity theory.

This book is an introductory text in General Relativity, while also focusing some solutions to the cosmological constant problem, which consists in an amazing 100 orders of magnitude discrepancy between the value of this constant in the present Universe, and its estimated value in the very early epoch. The author suggests that the constant is in fact, a time-varying function of the age of the Universe. The book offers a wealth of cosmological models, treats up to date findings, like the verification of the Lense-Thirring effect in the year 2004, and the recently published research by Cooperstock and Tieu (2005) suggesting that "dark" matter is not a necessary concept in order to explain the rotational velocities of stars around galaxies' nuclei. This is a mathematical cosmology textbook that may lead undergraduates, and graduate students to one of the frontiers of research, while keeping the prerequisites to a minimum, because most of the theory in the book requires only prior knowledge of Calculus and a University Physics course.