By the time readers reach the conclusion of this paean for a new science, they are likely to feel caught up in an exhilarating sense of space and time far removed from the Euclidean geometry of Newtonian physics--and equally far removed from relativity and quantum mechanics. This new science deals with hitherto intractable everyday complexity: weather forecasting, air and water turbulence, a faucet dripping, animal populations booming and crashing, epidemics of disease that come and go. It is a science because individuals have detected patterns, regularities, in these nonlinear dynamical systems--order in disorder. Discoveries came through multiple routes: a meteorologist studying convection, a mathematician studying oscillators, an ecologist modeling fecundity in fishes, in each case, the investigators decided to look at the global picture and how it varied depending on initial conditions. What they discovered was that chaos--aperiodicity and unpredictability--was dependent on initial conditions. What they further discovered was that there were unexpected cycles on the graphs of the equations. Often this required plotting hundreds or thousands of points with results that were unexpectedly breathtaking: the designs were beautiful. New York Times science writer Gleick is an excellent guide through this new discipline, chronicling the major acts of discovery and letting the actors speak. Many of them are mathematicians--Benoit Mandelbrot, Stephen Smale, James Yorke, Mitchell Feigenbaum--and it is interesting that so many have been mavericks or hybrid scientists for example, mathematical physicists disowned by both camps). This is not an easy book, because the ideas go against intuition and because so many paths can be traced in the development of the theory. These discontinuities have their own charms, however, as Gleick brings his characters on stage and discourses here on pendulums, there on the bronchial system of the lungs, and elsewhere on the infinities of the Cantor set. It will help to keep the baroque image in mind: Gleick makes the music of chaos soar, even if you can't always make out the individual notes.