Basic topics: Sample space, random variables, hope, transformations and limit theorems (law of large numbers and central limit theorem). Advanced topics: basic results of the measurement theory, changes in order between limits and hopes, normal multivariate distribution, conditional distribution and hope.
• James, Barry. Probability: An intermediate level course. IMPA. 2004;
• Blitzstein, Joseph and Hwang, Jessica. Introduction to Probability. 2014;
• Grimmett, Geoffrey and David Stirzaker. Probability and random processes. 3rd ed. Oxford University Press, 2001;
• Bertsekas, Dimitri and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008;
• DeGroot, Morris and Schervish, Mark. Probability and statistics. 4th ed. 2011
• Williams, David. Probability with Martingales. Cambridge University Press, 1991;