Much of the received economic analysis is concerned with markets characterized by centralized trading. In such markets the trades are carried out at openly announced prices and all traders have access to the same trading opportunities. In many important markets, however, the trading process is decentralized -- prices are quoted and transactions are concluded in private meetings among agents. This study develops a rigorous theory for this second type of market. It will involve construction and investigation of formal models of dynamic markets in which transactions are concluded in pairwise meetings between agents, and where agents are asymmetrically informed about the values of underlying parameters which will affect their eventual payoffs. This new theory of decentralized markets and asymmetric information is used to investigate the following questions: (1) How and to what extent is agents' information aggregated and transmitted via the trading process? (2) How is the allocation of resources affected by the underlying distribution of information transmission by the market? (3) Under what circumstances can the familiar paradigm of Rational Expectations Equilibrium (REE) be used to approximate the behavior of such markets? The significance of this research is that it will start to close a gap that exists in our understanding of markets. Although some important markets are characterized by decentralized trading, e.g., real estate markets and labor markets, to date practically the entire literature on markets with asymmetric information has been concerned with markets characterized by centralized trading. Preliminary work suggests that decentralized markets behave differently than centralized markets.