The existence of chaotic attracting sets has had an important impact in the natural sciences. As they have high sensitivity to initial conditions, an experimenter trying to repeat her/his experiment with all the knobs in the same positions will notice that repeated outputs differ from each other. For a discipline that has built its cultural power through history on reproducibility, this is quite a revolution. It is for this reason that we are going to study the structure of the solutions of three-dimensional flows: three is the minimal dimensionality in which chaotic phenomena occur (see chapter 6). In other words, the reader will not find other chapters dealing with 4-d flows, etc. Besides, the study of the structure of n-d flows with n > 3 is an open problem. Which of the tools used in this chapter to understand 3-d flows can be extended to higher dimensions might be an interesting question to keep in mind throughout these pages.