This is some great science writing for the general public. It explains chaos theory as both a scientific development and a social disruption in the culture of science. In the latter regard, it is heavily influenced by the work of Thomas Kuhn, whose concept of the disruptive 'paradigm shift' turned the social history of science on its head.
It's structured around portraits of scientists working alone or in small groups on problems that were considered esoteric, insoluble, a waste of time... and yet, mostly unbeknownst to one another, their ideas were converging towards a new conception of complex systems that, though based on simple repeating formulae, quickly became wildly complex. And there seemed to be analogues of it everywhere: in the weather, in the branching of ferns, in the crackle on telephone lines, in the dripping of a leaky faucet.
Mandelbrot's fractal geometry is the best known chaotic artifact to the non-scientist, because the visual images it produces are stunning. I have an app on my phone that explores the Mandelbrot set; it's mesmerizing. Like a lot of chaotic phenomena, computers are crucial in modeling it. But the fruits of chaos theory are everywhere. Weather prediction and storm tracking are highly reliant upon it. Hell, virtually every branch of science uses it now, from anthropolgy to zooology. Even I once referred to 'sensitivity to initial conditions' in a talk I gave on early intervention with visually impaired children, and I'm by no means a scientist. It's just a really useful framework for understanding a vast range of phenomena.
I pulled out an old college math text and reread the chapter on fractal geometry, though I didn't do the exercises. But it's really not necessary to understand much math to grasp the concepts. James Gleick is a first-rate explainer.
Entertaining, informative, a fun read. Highly recommended by me.