This first volume is dedicated to the memory of the late Professor Ivo G. Rosenberg (1934-2018) that is missed and recalled by the universal algebra and multiple valued logic communities not only as one of the greatest mathematicians of our time, but also as a wonderful human being. It is made of seven contributions that cover some of the many research interests of Ivo that include finite and infinite posets, lattices, tolerances, combinatorial properties of finite sets, matrices over lattices, and quasigroups and semigroups.