The paper presents a semi-analytic model for calculating the formation and evolution of galaxies in hierarchical clustering cosmologies, improving upon and extending the earlier scheme by Cole et al. (1994). The model uses a new Monte-Carlo algorithm to follow the merging evolution of dark matter halos with arbitrary mass resolution, incorporating realistic descriptions of density profiles, gas cooling, star formation, chemical evolution, and dust production. It also includes detailed calculations of disk and spheroid sizes. The model is fully specified and can be tested against observational data, showing good agreement with various properties of the local galaxy population. However, some discrepancies remain, such as the color-magnitude relation for ellipticals in clusters and the predicted galaxy circular velocities. The paper discusses the strengths and weaknesses of the model and its implications for understanding galaxy formation.The paper presents a semi-analytic model for calculating the formation and evolution of galaxies in hierarchical clustering cosmologies, improving upon and extending the earlier scheme by Cole et al. (1994). The model uses a new Monte-Carlo algorithm to follow the merging evolution of dark matter halos with arbitrary mass resolution, incorporating realistic descriptions of density profiles, gas cooling, star formation, chemical evolution, and dust production. It also includes detailed calculations of disk and spheroid sizes. The model is fully specified and can be tested against observational data, showing good agreement with various properties of the local galaxy population. However, some discrepancies remain, such as the color-magnitude relation for ellipticals in clusters and the predicted galaxy circular velocities. The paper discusses the strengths and weaknesses of the model and its implications for understanding galaxy formation.