The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of the critical properties of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Symposium was to provide an overview of the physical phenomena that manifest scale invariance and fractal properties with the aim of bringing out the common mathematical features. The emphasis was on theoretical and experimental work related to well defined physical phenomena.

(summary of): Preface. I. General properties of fractals. II. Analysis of fractal properties of materials. III. Polymer statistics and self-avoiding-walks. IV. Branched polymers, gelation and percolation. V. (A) Irreversible growth models: Laplacian fractals, dielectric breakdown, fracture propagation and viscous fingers in liquids. V. (B) Irreversible growth models: diffusion-limited aggregation, dendritic growth, Eden model and cluster-cluster aggregation. VI. Kinetics of clustering. VII. Dynamical properties of fractal structures. VIII. Hierarchical and fractal features of disordered systems. IX. Chaos, turbulence and related topics.