Chaos: Making A New Science is the best-selling book by James Gleick that first introduced the principles and early development of chaos theory to the public. It was a finalist for the National Book Award and the Pulitzer Prize in 1987.
The first popular book about Chaos Theory, it manages to explain the Mandelbrot Set, Julia Sets, Lorenz Attractors etc. without delving into the complex math. It also includes clear interesting descriptions of dozens of extraordinary and eccentric people—the individuals whose separate work converged on a new understanding. It remains in print and is widely regarded as still the best introduction and summary for someone who doesn't know much math.
Chaos: Making a New Science