The main goal of this one-week conference at the Fields Institute in London Ontario is to induce and stimulate interactions and collaborations at the cutting edge of research on noncommutative geometry and combinatorial C*-algebras. Its aim is also to celebrate the 90th birthday of Paul F. Baum whose remarkable contributions to mathematics, in particular noncommutative geometry, can hardly be overestimated. Better still, the meeting serves as the summarizing event of the European Union funded research network Operator Algebras That One Can See.