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The global climate of the Earth has significantly varied over the last millennia. On a regional scale, the climate has varied and does presently vary on many different time scales, leading to a continuously changing pattern of temperatures, humidity, precipitation, with important effects on the whole terrestrial biosphere. Physicist are interested in understanding the mechanism at work by gathering data and properly analysing them, by building theoretical models and, if possible, making predictions on the future evolution of the system. Along these lines, an important question is to understand the role of the solar forcing, in order to unravel the internal mechanisms of variability of the Earth's climate from the variable forcing of the Sun. On the other hand, one can learn about the past solar variability by reading into the terrestrial archives that provide us with proxy data on the history of both the Sun and the climate. Thus, realizing that the Sun and the Earth form a closely coupled system, where the variable properties of the former may affect in many subtle ways the behaviour of the latter, is an important step toward the understanding of both.This book is explicitly devoted to these issues. First, it is important to obtain reliable data from terrestrial archives, and to properly date the records that have been measured. The first part of the book is devoted to these crucial aspects, dealing with various types of proxy data and with the difficult issue of the dating of the records. Once obtained, the data has to be interpreted. This process nowadays relies upon a plethora of data analysis methods that explicitly take into account the nonlinear nature of the system and try to elucidate the dynamics and the main processes active in the measured system. The second part of the book is devoted to the issue of data analysis and prediction. Finally, once the data has been interpreted and analyzed, theoretical models have to be built describing the dynamics of the system considered. Due to the extreme complexity of the Sun/Earth system (as well as of its components, the Sun itself and the Earth's climate), drastic simplifications in the modelling efforts have to be accepted and one has to bear in mind that the models probably are nothing more than a pale image of the real dynamics. The third part of the book is devoted to the theoretical and numerical modelling of the solar and climatic variability, and of their complex interactions. This volume gives an up-to-date view of the present state of this field.