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.