The galaxy population appears to be composed of infinitely complex different types and properties at first sight. However, when large samples of galaxies are studied, it appears that the majority of galaxies just follow simple scaling relations while the outliers represent some minority. We demonstrate the astonishing underlying simplicities of the galaxy population emerged from large galaxy surveys and “reverse engineering” of the observed galaxy population at different epochs; derive the analytical forms for the dominant evolutionary processes that control the galaxy evolution via continuity equations. The further leap forwards is through the implementation of the “gas regulator model”, which takes into account the key physical processes of inflow, star formation, outflow， feedback and metal production, acts as the important linkage between the continuity framework and the cosmological framework of Lambda-CDM paradigm. By implementing the continuity framework into the cosmological context via the gas regulator model, we build a simple self-consistent global analytical framework to describe the formation and evolution of various galaxy population from DM haloes to gas and to the stellar population. This model will be a powerful tool to plan the observations with key forthcoming facilities such as JWST and MOONS.