This text discusses the basic ideas of complexity and chaos theories and presents many examples of architecture based on these ideas in the work of leading architects - Peter Eisenman, Frank Gehry, Renzo Piano, Charles Correa and Itsuko Hasegawa - along with ecological and organic designs. Charles Jenck"s own recent work is used to illustrate concepts in physics and an architecture based on waves and twists. This work both advocates and criticizes as it seeks to define a new direction for the contemporary arts.