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Here I would like to share some selected notes that I wrote along my path of mathematical learning and research over the past years. Most of the topics are classical and fundamental. This is mainly for the benefit of students.

• The Mathematical Theory of Moment Generating Functions
• The Wiener-Itô Chaos Decomposition and Multiple Wiener Integrals
• Integration on Groups and Non-abelian Fourier Analysis
• Lecture Notes on Advanced Probability
• An Introductory Course on Stochastic Calculus
• An Introduction to the Theory of Rough Paths