We describe the GALFORM semi-analytic model for calculating the formation and evolution of galaxies in hierarchical models. It improves upon, and extends, the Cole et al 1994 model. The model employs a new Monte-Carlo algorithm to follow the merging evolution of dark matter halos with arbitrary mass resolution. It incorporates realistic descriptions of the density profiles of dark matter halos and their gas content; follows the chemical evolution of gas and stars, and the associated production of dust; and includes a detailed calculation of the sizes of disks and spheroids. Wherever possible, our prescriptions for modelling individual physical processes are based on results of numerical simulations. We apply our methods to the LCDM cosmology (Omega_0=0.3, Lambda_0=0.7), and find good agreement with a wide range of properties of the local galaxy population: the B-band and K-band luminosity functions, the distribution of colours for the population as a whole, the ratio of ellipticals to spirals, the distribution of disk sizes, and the current cold gas content of disks. (Abridged)
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