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.