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A-SLOTH (Ancient Stars and Local Observables by Tracing Halos) connects the formation of the first stars and galaxies to observables. The model is based on dark matter merger trees, on which A-SLOTH applies analytical recipes for baryonic physics to model the formation of both metal-free and metal-poor stars and the transition between them. The software samples individual stars and includes radiative, chemical, and mechanical feedback. A-SLOTH has versatile applications with moderate computational requirements. It can be used to constrain the properties of the first stars and high-z galaxies based on local observables, predicts properties of the oldest and most metal-poor stars in the Milky Way, can serve as a subgrid model for larger cosmological simulations, and predicts next-generation observables of the early Universe, such as supernova rates or gravitational wave events.