275A: Probability Theory - Terence Tao's course notes
by Terence Tao · UCLA
Where Durrett gives one canonical proof, Tao gives three - characteristic functions, the moment method, and the Lindeberg exchange - and explains what each buys you. That comparative view is what turns the CLT from a memorised theorem into a technique you can transfer. Six sets of graduate lecture notes with exercises, building from measure-theoretic foundations to Notes 3 on the weak and strong laws, Notes 4 on the central limit theorem, and Notes 5 on variants including Berry-Esseen and stable laws.
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