This study presents a Formal General Design Theory (FGDT), a mathematical theory of design. The main goal of FGDT is to lay out a domain independent modeling of design artifacts (`Part I') and the design process (`Part II'). We discuss issues such as: the scope of the theory with respect to real design and the guidelines it provides for building CAD systems, representation of design artifacts, idealized design process cycle, and computational complexity analysis. Treating FGDT as a model aims at developing a generally accepted core of design theory. We also point out the possibilities that such a model opens in terms of studying conceptual design (for example, modeling the relation between design and quality).