Universality is the property that systems of radically different composition and structure exhibit similar behavior. The appearance of universal laws in simple critical systems is now well established experimentally, but the search for universality has not slackened. This book aims to define the current status of research in this field and to identify the most promising directions for further investigations. On the theoretical side, numerical simulations and analytical arguments have led to expectations of universal behavior in several nonequilibrium systems, e.g. aggregation, electric discharges, and viscous flows. Experimental work is being done on "geometric" phase transitions, e.g. aggregation and gelation, in real systems. The contributions to this volume allow a better understanding of chaotic systems, turbulent flows, aggregation phenomena, fractal structures, and quasicrystals. They demonstrate how the concepts of renormalization group transformations, scale invariance, and multifractality are useful for describing inhomogeneous materials and irreversible phenomena.