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Galaxies are thought to reside inside of large gravitationally bound structures of dark matter, so-called haloes. While the smallest of these haloes host no or only a few stars, the biggest host entire clusters of galaxies. Over cosmic history, haloes often collided and merged, forming bigger and bigger structures. Merger trees, i.e., catalogues of haloes evolving and connections between them as they grow and merge, have become a vital tool in describing and understanding the history of cosmological objects such as our Galaxy. Semi-analytical models, built on top of such merger trees, are a common approach for theoretical studies in cosmology. The semi-analytical nature of such models is especially beneficial when the dynamic range in spatial and time scales that need to be considered becomes too large for numerical simulations. Ancient Stars and Local Observables by Tracing Halos (A-SLOTH) is such a semi-analytical model and it is designed to simulate star formation in the early Universe in a fast and accessible way. It uses merger trees, either from numerical simulations or generated by statistical algorithms to describe the history of galaxies. The processes of baryonic physics, in particular gas cooling, star formation and stellar feedback are described with approximations and statistical models. The range of applications for this model is extensive and we, therefore, make it available to the scientific community.