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Based on the author's extensive teaching experience, this book covers topics of classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity. It addresses major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background and inflation introduces the setting for the phenomenological application of various quantum gravity and string theory approaches to cosmology. Born from the author's commitment to bridging the gap between cosmologists and theoreticians at the frontier of quantum gravity, this volume aims to be a learning text for undergraduate and graduate students as well as a reference for lecturers and researchers.§