Probability Theory
Probability measures and randown variables, pi and lambda systems, expectation, the moment generating function, the characteristic function, laws of large numbers, limit theorems, conditional contribution and expectation, martingales, infinitely divisible laws and stable laws.
Recommended Books
Durrett, R., Probability: Theory and Examples, 4th edition, Cambridge University Press, 2010.
Billingsley, P., Probability and Measure, 3rd Edition, Wiley India, 2008.
Kallenberg, O., Foundations of Modern Probability, 2nd edition, Springer-Verlag, 2002.
Walsh, J., Knowing the Odds: An Introduction to Probability, AMS, 2012.