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Recently, non-commutative generalizations of lattices and related structures have seen an upsurge in interest, with new ideas and applications emerging, from quasilattices to skew Heyting algebras. Much of this activity derives in some way from the initiation, thirty years ago, by Jonathan Leech, of a research program into structures based on Pascual Jordan-s notion of a non-commutative lattice. The first workshop on non-commutative structures aims to present the breadth of contemporary research in the area, with contributions from international and Slovenian mathematicians. We are delighted that Jonathan Leech has accepted our invitation to deliver the keynote address in this meeting, which will hopefully be the first of many.