Abstract: We study a class of heterogeneous economic models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and transformations. A basic guiding principle is gauge invariance, which means that the dynamics of the economy should not depend on the units each product is measured. We develop a covariant theory of perturbations around equilibrium. With this we are able to study the stability of some exchange equilibria, and the role of the trading network topology in the relaxation time. We also study some simple models of both centralized and decentralized markets. In particular, we present a simple model of a decentralized market that shows a spontaneous transition into a monetary phase. We use mean field theory analysis to provide a statistical interpretation of the monetary phase. Furthermore, we show that such phase can be dynamically unstable. Finally, we study some simple centralized financial markets, one of which shows a speculative bubble and a crash.