This book is devoted to the field of basin analysis, and in particular to the one- and two-dimensional modeling of the burial, thermal and maturation histories of sedimentary basins, in the context of evaluating their hydrocarbon potential. A new modeling system is elaborated in this work and applied to continental basins. Particular attention is paid to specific features of basin evolution, including the compaction of sediments deposited at a variable rate, erosion of the sedimentary strata and basement, intrusive and hydrothermal activity, thermal activation and reactivation of the basement, lateral heat exchange of multiple-aged blocks of the oceanic and continental lithospheres, the jumping of spreading axes, etc. Alternative methods are applied for the control of tectonic subsidence, isostasy and rheology, lithosphere stretching and thinning. In order to evaluate their respective contributions to the thermal history of basins, a variety of situations are modeled, including spreading jumping, the evaluation of erosion heat, its impact on thermal history and links to pre- and post-sedimentation history, intrusion activity, and the formation and degradation of cryolitic zones (permafrost) in high-latitude basins of the Northern and Southern Hemispheres. A joint analysis of heat flow transfer in the sedimentary cover and the underlying lithosphere and asthenosphere is applied to better reconstruct their thermal and maturation histories. To further enhance the model's validity, an additional powerful control tool is applied, based on the coincidence of two calculations of tectonic curve subsidence of the basement surface, obtained by two independent approaches: backstripping and temperature-dependant density distribution in the crust. This approach is also used to refine the simulation sequence for tectonic and thermal events in the history of sedimentary basins.