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This course will be in two parts the first will cover the basics of real analysis. This part will begin with the elementary elements of real analysis: sets, sequences, functions and continuity. It will then move on to the properties of Topological, Normed and Metric and Linear spaces. Aspects of this theory that are of particular importance to Economics will be emphasi¿e, notably fixed-point theory, convexity, the maximum theorem, and dynamic programming. The second part of the course will cover the basics of measure and probability theory. It will begin with the basics of measure theory, random variables, integration (Lebesgue and Stieltjes). It will then move on to notions of convergence, sequences of random variables, probability limit theorems (weak, strong, Borel-Cantelli, 0-1 Laws) , conditional expectation and martingales. In future versions it would be desirable to have some treatment of continuous state stochastic processes. This course will be based on two well-established texts. Real Analysis with Economic Applications, Efe A. Princeton University Press, Probability with Economic Applications, Efe A, Online editions of both texts exist. Further reading will include, A Course in Real Analysis, J. N. McDonald and N.A Weiss,Probability and Measure, P. Billingsley.