The theory of design spaces is based on Yoshikawa s work on mathematical theory of design, which was developed in Japan in the 1970s and first presented in English in 1981 [1]. The theory was further developed by Yuzuru Kakuda and Makoto Kikuchi and their colleagues; see for example, [2]. Although the theory may be still far from mature to capture all aspects of design, it presents a good starting point towards a mathematical foundation of the scientific discipline of design. Here, this chapter is only an informal introduction to the basic ideas of the theory, rather than the mathematical treatment of the subject. An introduction to the theory and a critical review of recent developments in the direction can be found in [5].

The design space of software architectural elements is based on Kazman, Clements, Abowd and Bass s work on classification of software architectural elements [4]. Another important work on the classification of software architectural elements is by Melta, Medvidovic and Phadke [6], which is devoted to connectors. The design space of software architectural styles is based on Shaw and Clements s work on the classification of software architectural styles [7].