WITCH - World Induced Technical Change Hybrid - is a regionally disaggregated hard-link hybrid global model with a neoclassical optimal growth structure (top-down) and a detailed energy input component (bottom-up). The model endogenously accounts for technological change, both through learning curves that affect the prices of new vintages of capital and through R&D investments. The model features the main economic and environmental policies in each world region as the outcome of a dynamic game. WITCH belongs to the class of Integrated Assessment Models as it possesses a climate module that feeds climate changes back into the economy. Although the model's main features are discussed elsewhere (Bosetti et al., 2006), here we provide a more thorough discussion of the model's structure and baseline projections, to describe the model in greater detail. We report detailed information on the evolution of energy demand, technology and CO2 emissions. We also explain the procedure used to calibrate the model parameters. This report is therefore meant to provide effective support to those who intending to use the WITCH model or interpret its results.