The _right_ way of proving Gronwall's inequality.

Terry Tao discusses the work of the four 2010 Fields medal winners.

Terry Tao's course on random matrices.

"These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces." Useful stuff, seeing as how the machinery of analytic sets and standard Borel spaces is used to justify the manipulations with suprema over uncountable sets in the theory of empirical processes, as well as the reduction of partially observed MDPs in general spaces to fully observed MDPs on the space of hyperstates.

William P. Thurston

by Terry Tao

Terry Tao explains the recent paper by Robin Moser.

From the abstract: "[Marx] regarded questions about the foundations of the differential calculus as a "touchstone of the application of the method of materialist dialectics to mathematics." Nearly a century later, Chinese mathematicians explicitly linked Marxist ideology and the foundations of mathematics through a new program interpreting calculus in terms of nonstandard analysis."

by Glenn Shafer and Vladimir Vovk

by A. Juditsky and A. Nemirovski

Lecture notes by Roman Vershynin (UC Davis)

Mark Rudelson and Roman Vershynin

(as in Johnson-Lindenstrauss)

Terry Tao's course on ergodic theory. Mmmmmm, measure-preserving...

book by Pascal Massart: contains stuff on minimum-contrast estimators

FOCS 2008 tutorials (Terry Tao on randomness in combinatorics; Dan Boneh on crypto; Dan Spielman on graph spectra)

Lecture notes on measure concentration by A. Barvinok (PDF)

Lecture notes by Ryan O'Donnell (CMU)