This volume contributes to the debate on the application, in the disciplines of architecture and urbanism, of new formal methods and methodological advances based on tools from mathematics. From millennial geometry to current shape grammars, several formal approaches to architecture and urbanism are presented here, in order to look at the potentials and purposes of these formal methods, both those on the horizon and those already accomplished. This book promotes the use of formal methods in the creation of new explicit languages for problem-solving in the field. This collection of papers will help students, academics, researchers, and practitioners developing formal methods towards the digitalization of the architecture and urbanism sector.