Nonlinearity is the source of complexity. It gives rise to the change of the system behaviors, the evolution of structures and such phenomena as bifurcation, catastrophe, and even chaos. It is these phenomena, dovetailed with others, that weave out our multicolor and multifold world synergentically. With the development of science and technology, people become more and more interested in and capable of the study of nonlinearity so as to shed light on the nature of the world. In order to deal with nonlinearity more systematically, this paper elaborates a comprehensive description for the dynamical system. Then, we focus on the relationships between the characters of nonlinearity. We have successfully expounded some controversial concepts, cast new light on some important relations, and unified several concepts which are the central topics of many modern theories.