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.
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