7 Probability
I assume that you have seen some probability theory before, and that this is just a reminder. If you need a more thorough refresher, the book by Ross (Ross 2014) is a popular introductory text that covers discrete and continuous problems, but not more general probability measures. Another good undergraduate text by Chung and AitSahlia (Chung and AitSahlia 2003) includes a little bit of measure theory. Good graduate texts include the books by Billingsley (Billingsley 1995) and by Breiman (Breiman 1992). If you want a reminder that is more thorough than the one we give here, but less than a full textbook, the treatment in (Deisenroth, Faisal, and Ong 2020) is a good starting point.
Axiomatic probability, counting, and measure
Conditional and marginal probabilities
Bayesian and frequentist perspectives
Random variables
The wonder of Gaussians (and not all RVs are Gaussian!)
Moments (+ linearity of expectations, variance and precision,heteroscedasticity, etc) and tails
Independence, conditional independence, factorization of probabilities, graphical models
Standard statistics (incl variance and precision)
Central limit theorem / LLN / sums
Parameter estimation
Bayes and updating
Conjugate priors
Uninformative priors
Markov chains
Martingales
Stochastic processes
Standard inequalities and concentration of measure