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 vast majority of galaxies just follow simple scaling relations and similar evolutional modes while the outliers represent some minority. We demonstrate the astonishing underlying simplicities of the galaxy population emerged from large surveys and take a new approach to the topic of galaxy evolution and derive the analytical forms for the dominant evolutionary processes that control the galaxy evolution. This model successfully explained the observed evolution of the galaxy stellar mass functions (GSMF) of both passive and star-forming galaxies and the origin of the Schechter form of the GSMF. The model also offers natural explanations for the "anti-hierarchical" age-mass relation and the alpha-enrichment patterns for passive galaxies and makes many other testable predictions, such as the mass function of the population of transitory objects that are in the process of being quenched, the galaxy major- and minor-merger rates, the galaxy stellar mass assembly history, star formation history etc. Although still purely phenomenological, the model makes clear what the evolutionary characteristics of the relevant physical processes must in fact be. This model thus offers a new powerful analytical framework to study galaxy evolution and to explore a number of crucial issues and questions in galaxy evolution.