Abstract: This paper studies the existence and characterization of optimal solutions to the principal-agent problem with adverse selection for both discrete and continuous problems. The existence results are derived by the abstract concepts of differentiability and convexity. It is known that under the Spence Mirrlees condition, the principal-agent problem can be reduced to a simpler problem which can be solved explicitly. But not much results on the solution are known when the Spence Mirrlees condition does not hold. For the problem without the Spence Mirrlees condition, we give some sufficient conditions to verify the linear independence and the Mangasarian Fromovitz constraint qualification.