Relatively small climate fluctuations, such as the warming period that was observed in recent decades, occur over periods of tens and hundreds of years, and are called near-term climate fluctuations. More significant climate changes occur over periods of tens of thousands of years, and they are called long-term climate changes. As a result of the interaction of the Earth with the Moon, the Sun and the planets, the orbital and rotational movements of the Earth are evolving. The orbit itself rotates counter-clockwise in its plane, making a complete revolution in 147 thousand years, and its axis makes one revolution in 68.7 thousand years around a certain direction. The axis of rotation of the Earth also rotates clockwise in 25.7 thousand years around another direction. In addition, these axes also exercise oscillatory movements. As a result of the evolution of these movements, the insolation of the Earth and, consequently, the Earth’s climate undergo changes. These long-term changes in the Earth’s insolation are analyzed in the astronomical theory of climate change, first proposed by M. Milankovich almost one hundred years ago. This book presents a new version of this theory. In contrast to the previous version, the problems concerning the evolution of the orbital and rotational movements of the Earth are solved here in a different way, with new results obtained. These new results coincide with observations and with the warming and cooling periods that took place in the Earth’s history. This book is intended for a wide range of readers of different specialties and ages. It can be used by both undergraduate students and graduate students in preparation of their term papers and dissertations.