Basically, there are three key ideas that keep reappearing throughout the book. Each idea is relatively simple in principle, but all three must be presented within the context of the entire book in order to be appreciated since all of them make some reference to the contents of the five book parts: computation, fractals, chaos, complex systems, and adaptation.

Taken in order, these three ideas roughly build on one another, so it helps to consider them in the following order:

1. The whole is greater than the sum of the parts

By this I mean that the topics of computation, fractals, chaos, complex systems, and adaptation are far more interesting considered together than by themselves. Each of the topics is related to the others in a non-trivial way; moreover, each can be seen as the result of a few simple principles such as recursion, parallelism, and nonlinearity.

2. The interesting stuff is in the middle

``Beauty,'' i.e., that which makes something interesting, is related to a mixture of regularity and irregularity. When things are too regular, we usually find them to be uninteresting because they yield no surprises for us. Complementary to this, highly irregular things are often uninteresting because they make no sense. In the middle, between regularity and irregularity, lies a place where things can be understood, but not completely.