In this book rigorous mathematical techniques are used to compare the Islamic financial system based on variable return scheme (VRS) with the traditional one based on fixed return scheme (FRS). It is shown, under certain assumptions which include risk aversion on the part of investors, that the Pareto optimal contract is the VRS. Also VRS spreads risks more evenly than FRS allowing more risk taking in the economy. The domination of the real world by FRS, i.e. debts contracts, is shown to be caused mainly by informational asymmetry and higher monitoring Costs in case of VRS. But these costs are not prohibitive. The more effective the methods of monitoring and the higher the level of honesty on the part of economic agents, the more superior the Islamic financial system would prove to be in practice.