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This paper describes the WITCH-World Induced Technical Change Hybrid-model in its structure, calibration, and the implementation of the SSP/RCP scenario implementation. The WITCH model is a regionally disaggregated hard-linked model based on a Ramsey type optimal growth model and a detailed bottom-up energy sector model. A particular focus of the model is the modeling or technical change and RnD investments and the analysis of cooperative and non-cooperative climate policies. Moreover, the WITCH 2016 version now includes land-use change modeling based on the GLOBIOM model, and air pollutants, as well as detailed modeling of the transport sector and the possibility for stochastic modeling. This version has been also used to implement the Shared Socioeconomic Pathways (SSPs) set of scenarios and RCP based climate policies to provide a new set of climate scenarios. In this paper, we describe in detail the mathematical formulation of the WITCH model, the solution method and calibration, as well as the implementation of the five SSP scenarios. This report therefore provides detailed information for interested users of the model, and for understanding the implementation of the different" worlds" of the SSP.