It introduces the research tradition of computational approaches to design from historical, mathematical and aesthetic perspectives and develops a standard framework for understanding the role of production methods in the creative processes of design (synthesis and analysis). Basic mathematical concepts of artificial languages and computational systems are explained, and historical reference is made to specific computational approaches to design (Alexander, March, Hillier, Stiny). Specific modes of description and production such as parametric models, typology, and grammar are explained. Emphasis is placed on grammars, whose computational and expressive capabilities are contrasted with other algorithmic systems. Basic concepts such as Euclidean transformations, symmetry, spatial relations, generative rules and axiomatic schemes, scheme arithmetic and the algebras Ui j, Vi j and Wij are introduced. The concepts of form, structure, and composition are analyzed. The relationships of the grammatical approach to cognitive areas such as music, aesthetics, philosophy of science, linguistics, psychology, literature, history, mathematics, mathematical logic and artificial intelligence are examined.