ASTRAEUS (semi-numerical rAdiative tranSfer coupling of galaxy formaTion and Reionization in n-body dArk mattEr simUlationS) self-consistently derives the evolution of galaxies and the reionization of the IGM based on the merger trees and density fields of a DM-only N-body simulation. It models gas accretion, star formation, SN feedback, the time and spatial evolution of the ionized regions, accounting for recombinations, HI fractions and photoionization rates within ionized regions, and radiative feedback. ASTRAEUS is for studying the galaxy-reionization interplay in the first billion years. The underlying code is written in C and is MPI-parallelized; its modular design allows new physical processes and galaxy properties to be added easily. ASTRAEUS can be run on a tree-branch-by-tree-branch basis (i.e., fully vertical) or on a redshift-by-redshift basis (i.e., fully horizontal) when evolving the galaxies by using local horizontal merger trees.