This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods--based on asymptotic, probabilistic, and group-theoretic standpoints--are used to examine experimental and computational data from numerous examples (e.g., soil, sand, kaolin, concrete, domes, etc.). Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory. For mathematicians, static bifurcation theory for finite dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples.