Digital preservation is a pressing challenge to the library community. In this paper, we describe the initial results of our efforts towards understanding digital (as well as traditional) preservation problems from first principles. Our approach is to use the language of mathematics to formalize the concepts that are relevant to preservation. Our theory of preservation spaces draws upon ideas from logic and programming language semantics to describe the relationship between concrete objects and their information contents. We also draw on game theory to show how objects change over time as a result of uncontrollable environment effects and directed preservation actions. In the second half of this paper, we show how to use the mathematics of universal algebra as a language for objects whose information content depends on many components. We use this language to describe both migration and emulation strategies for digital preservation.