The market system consists of a price mechanism, built on the foundation of a system of property, and contract. In many developing, and transition economies, the market system functions poorly. In many cases, if not most, the malfunctioning is not simply in the price system (for example, anti-competitive activities), but in the underlying property system (such as contracts being breached, and externalities in the sense of transfers not covered by contracts). Economic theory tends to take the functioning of the system of property, and contract for granted, and focuses on the operation of the price mechanism. Property theory focuses on the underlying system of property, and contract. In this paper, the author inaugurates the mathematical treatment of property theory. In contrast with earlier work in "law and economics", and the "new institutional economics", this approach uses principles drawn from jurisprudence, and does not attempt to reduce "law" to "economics" in the sense of efficiency considerations, such as the minimization of transaction costs. The main results are the two fundamental theorems of property theory that are analogous to the two fundamental theorems of price theory that, in essence, state that: 1) A competitive equilibrium is Pareto optimal. 2) Given a Pareto optimal state, there exists a set of prices such, that a competitive equilibrium at those prices would realize that Pareto optimal state
