A qualitative and quantitative frameworks for the fundamental theory of system science as well as some details are given on the basis of some new experimental evidences, ideas and achievements concerning evolution in many fields such as modern physics, molecule biology and brain anatomy, etc. Some concepts such as interaction, evolution, adaptability, and complexity are discussed. Intuitional annot ationsabout catastrophe, bifurcation, attractor, chaos, fractal and synergy are also given. The essence and t...