The common topic of the eleven articles in this volume is ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This emerging field of study is found at the crossroads of algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. The volume brings together contributions by leading specialists. Important advances in understanding the foundations of this new field are presented.
Similarity submodules and semigroups by M. Baake and R. V. Moody Pisot-cyclotomic quasilattices and their symmetry semigroups by D. Barache, B. Champagne, and J.-P. Gazeau Three possible branches of determinate modular generalization of crystallography by N. A. Bulenkov Non-crystallographic root systems by L. Chen, R. V. Moody, and J. Patera Upper bounds for the lengths of bridges based on Delone sets by L. W. Danzer The local theorem for tilings by N. P. Dolbilin and D. W. Schattschneider Uniform distribution and the projection method by A. Hof One corona is enough for the Euclidean plane by D. W. Schattschneider and N. P. Dolbilin Cut-and-project sets in locally compact Abelian groups by M. Schlottmann Spectrum of dynamical systems arising from Delone sets by B. Solomyak Non-locality and aperiodicity of $d$-dimensional tilings by G. van Ophuysen.