The GALFORM semi-analytic model describes the formation and evolution of galaxies in hierarchical clustering cosmologies. It improves upon and extends the earlier scheme by Cole et al. (1994). The model uses a new Monte-Carlo algorithm to track the merging evolution of dark matter halos with arbitrary mass resolution. It incorporates realistic descriptions of dark matter halo and gas density profiles, models chemical evolution of gas and stars, and calculates disk and spheroid sizes. Prescriptions for physical processes are based on numerical simulations and adjusted using local galaxy data. The model is applied to the ΛCDM cosmology (Ω₀=0.3, Λ₀=0.7) and shows good agreement with local galaxy properties. Discrepancies remain, such as the flatter colour-magnitude relation for ellipticals in clusters and higher predicted circular velocities. The model suggests over half the universe's stars formed since z ≲ 1.5. The paper discusses the model's methods, including merger tree generation, halo properties, and galaxy formation processes. It highlights the model's strengths and limitations, and compares results with observational data. The model uses semi-analytic techniques to simulate galaxy formation, incorporating chemical enrichment, dust processes, and halo merger histories. It provides a framework for understanding galaxy evolution and testing against observational data. The model's predictions are validated against various galaxy properties, including luminosity functions, Tully-Fisher relations, and star formation histories. The paper concludes that the model is a valuable tool for studying galaxy formation and evolution in cosmological contexts.The GALFORM semi-analytic model describes the formation and evolution of galaxies in hierarchical clustering cosmologies. It improves upon and extends the earlier scheme by Cole et al. (1994). The model uses a new Monte-Carlo algorithm to track the merging evolution of dark matter halos with arbitrary mass resolution. It incorporates realistic descriptions of dark matter halo and gas density profiles, models chemical evolution of gas and stars, and calculates disk and spheroid sizes. Prescriptions for physical processes are based on numerical simulations and adjusted using local galaxy data. The model is applied to the ΛCDM cosmology (Ω₀=0.3, Λ₀=0.7) and shows good agreement with local galaxy properties. Discrepancies remain, such as the flatter colour-magnitude relation for ellipticals in clusters and higher predicted circular velocities. The model suggests over half the universe's stars formed since z ≲ 1.5. The paper discusses the model's methods, including merger tree generation, halo properties, and galaxy formation processes. It highlights the model's strengths and limitations, and compares results with observational data. The model uses semi-analytic techniques to simulate galaxy formation, incorporating chemical enrichment, dust processes, and halo merger histories. It provides a framework for understanding galaxy evolution and testing against observational data. The model's predictions are validated against various galaxy properties, including luminosity functions, Tully-Fisher relations, and star formation histories. The paper concludes that the model is a valuable tool for studying galaxy formation and evolution in cosmological contexts.