This volumes gives a complete description of the Universe's birth and evolution, based on the implementation of General Relativity and Quantum Field Theory. The presentation has a pedagogical profile and aims to make accessible, at a Master's Degree level, a wide number of subtle topics concerning the thermal history of the Universe. This also includes the discussion of themes still open to the scientific debate, such as the quantum nature of the cosmological singularity and the nature of the dark components of the Universe. To this aim, this volume is divided into three parts, the first two being dedicated to introducing the paradigms of Einsteinian gravitation and quantum physics. These are necessary for a self-consistent presentation of the third part which fully develops the analysis of the cosmological framework. The first two parts have their own independent value as compact, pedagogical introductions to the corresponding areas, and are completed by relevant monographic appendices. In this respect, the picture outlined in the two chapters devoted to quantum physics of gravitation is distinguished by the clear and complete synthesis it offers to the reader. The main targets of this volume are Master's Degree students; however, because of the advanced character of some selected topics, it can also be fruitfully adopted by PhD students and even researchers wishing to obtain an up-to-date knowledge of some of the topics addressed in the book.