Merger Trees uses a Monte Carlo algorithm to generate merger trees describing the formation history of dark matter haloes; the algorithm is implemented in Fortran. The algorithm is a modification of the algorithm of Cole et al. used in the GALFORM semi-analytic galaxy formation model (ascl:1510.005) based on the Extended Press–Schechter theory. It should be applicable to hierarchical models with a wide range of power spectra and cosmological models. It is tuned to be in accurate agreement with the conditional mass functions found in the analysis of merger trees extracted from the Λ cold dark matter Millennium N-body simulation. The code should be a useful tool for semi-analytic models of galaxy formation and for modelling hierarchical structure formation in general.