In 1966, E.H. Lieb and D.C. r1attis published a book on "Mathematical Physics in One Dimension" [Academic Press, New York and London] which is much more than just a collection of reprints and which in fact marked the beginnings of the rapidly growing interest in one-dimensional problems and materials in the 1970's. In their Foreword, Lieb and r~attis made the observation that " ... there now exists a vast literature on this subject, albeit one which is not indexed under the topic "one dimension" in standard indexing journals and which is therefore hard to research ... ". Today, the situation is even worse, and we hope that these Proceedings will be a valuable guide to some of the main current areas of one-dimensional physics. From a theoretical point of view, one-dimensional problems have always been very attractive. Many non-trivial models are soluble in one dimension, while they are only approximately understood in three dimensions. Therefore, the corresponding exact solutions serve as a useful test of approximate ma thematical methods, and certain features of the one-dimensional solution re main relevant in higher dimensions. On the other hand, many important phe nomena are strongly enhanced, and many concepts show up especially clearly in one-dimensional or quasi -one-dimensional systems. Among them are the ef fects of fluctuations, of randomness, and of nonlinearity; a number of in teresting consequences are specific to one dimension.

Inhalt
I. Introductory Lecture.- How to Reduce Practically Any Problem to One Dimension.- II. Solitons.- An Overview of Soli ton Mathematics.- Statistical Mechanics of Soli tons.- The Quantum Inverse Scattering Method and Applications to Spin Chains.- Bethe Ansatz, Connection Between One-Dimensional Models and Their Classification.- Quantum Statistics of Soli tons.- Classical Statistical Mechanics of Soliton-Bearing Systems.- Multistable Driven Systems.- Inherent Effects of Discretization in an Interacting Kink-Phonon System.- Ising Models, Solitons, and the Devil's Staircase.- III. Magnetic Chains.- Quantum Spin Chains.- Dynamic Correlations in Classical Heisenberg Chains.- Dynamics of One-Dimensional Magnets: Neutron Scattering Studies.- Solitons in One-Dimensional Magnets with Various Symmetries.- A Comparison of Static and Dynamic Properties of One-Dimensional Magnets and Corresponding sG Systems.- Evidence for Soliton Excitations in the One-Dimensional Antiferromagnet TMMC.- Quantum Effects in the Dynamics of the One-Dimensional Planar Antiferromagnet.- Ground-State and Local Excitations in Co(PYR)2Cl2.- New High-Field Phenomena in Spin-Peierls Systems.- IV. Polymers.- Solitons in Polyacetylene: A Summary of Experimental Results.- Magnetic Resonance Studies of Soliton Diffusion in Polyacetylene.- Theory of Polymers Having Broken Symmetry Ground States.- Attracting Solitons and a First Order Lock-In Transition: Metallic Polyacetylene and the Spin-Peierls System.- Polyacetylene Revisited.- Magnetic Behavior of Polyacetylene, Polyparaphenylene and Polypyrrole.- Static and Dynamic Susceptibilities of Magnetic Polymers.- V. Quasi-One Dimensional Conductors.- Structural Ordering in Quasi-One-Dimensional Systems.- One-Dimensional Metals: Theory versus Experiment.- ElectronicInstabilities in Quasi-One-Dimensional Conductors: Insulator or Superconductor?.- Non-Linear Transport in the Fröhlich Mode Conductor, NbSe3.- VI. Disorder and Localization.- Lattice Dynamics and Spectral Properties of Disordered Chains.- Excitation Dynamics in Random One-Dimensional Systems.- Random Exchange Spin Chains.- Universality in Quantum Random Magnetic Chains.- Localization in One Dimension.- Localization in Thin Wires.- Transport Quantities in One-Dimensional Disordered Systems.- VII. Superionic Conductors, Coulomb Systems, Molecular Systems and Fractals.- One-Dimensional Superionic Conductors.- One-Dimensional Coulomb Systems.- Exciton Dynamics in Quasi-One-Dimensional Molecular Systems.- Critical Phenomena and Fractals with Dimensionality Near 1.- Index of Contributors.