Design is done in many fields. Although the design practices in different fields appear to be distinct from each other, all fields use a common thought process and design principles. Consequently, the true differences between these fields are minor, often consisting of the definitions of words, the specific data, and knowledge. In comparison, larger differences can exist within a given field between simple systems and large systems due to the size and the time dependent nature of functional requirements. The axiomatic approach to design provides a general theoretical framework for all these design fields, including mechanical design. The key concepts of axiomatic design are: the existence of domains, the characteristic vectors within the domains that can be decomposed into hierarchies through zigzagging between the domains, and the design axioms (i.e., the Independence Axiom and the Information Axiom). Based on the two design axioms, corollaries and theorems can be stated or derived for simple systems, large systems, and organizations. These theorems and corollaries can be used as design rules or guidelines for designers. The basic concepts are illustrated using simple mechanical design examples. When design is viewed axiomatically, not only product design but all other designs, including design of process, systems, software, organizations, and materials, are amenable to systematic treatment.