It was almost four hundred years ago that Galileo wrote in Il Saggiatore
that the "Book of Nature is written in mathema ti ca 1 characters". Thi
s sentence, i nspi red at the dawn of physics has proved with the
passage of time to contain a deep truth and also a warning: in order to
understand Nature, first we must learn to read mathema- tical
characters. Indeed, writing physical law in such characters has proved
not as hard as unraveling the content of the resulting equations. In
particular, the lack of knowledge in the field of nonlinear mathematics
has been a severe limita- tion in the past. Thus the solution to
equations such as the Navier-Stokes equation in fluid dynamics has
remained elusive. The recent advent of fast computers and some important
analytical and numerical results in the study of bifurcations and
nonlinear waves have encouraged work both in theory and experiment
involving non- linear phenomena. An explosive growth in the specialized
literature penetrating most research areas in physics in the last few
years has ensued. This book contains the most recent advances in
nonlinear physics in various fields including astrophysics, gravitation,
particle physics, quantum optics, fluid dynamics and the mathematics
underlying the phenomena of chaos and nonlinear waves. It presents a
selection from the lectures delivered at the XXI '_atin American School
of Physics held in Santiago, Chile in July-August 1984 (EtAF'84).