Probability Theory
Probability measures and random variables, pi and lambda systems, expectation,
moment generating function, 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.

Killenberg, O., Foundations of Modern Probability, 2nd Edition, Springer-
Verlag, 2002.

Walsh, J., Knowing the Odds: An Introduction to Probability, AMS, 2012.