The note is based on Chapter 2,3,5,6 of Stein’s book Fourier Analysis: An Introduction, which is an elegant book for undergraduates majoring in mathematics, especially the beginners with basic knowledge of Mathematical Analysis. I read the book after my first year of math learning and it really invoked my interest of further analysis, because you can easily find its applications in solving wave equations and heat equations by just using Fourier transformation on those equations, what a useful tool!

On April tenth, 2025, I gave a small talk in Complex Analysis(H)(English), and the second PDF is my draft which includes the third topic in Ch4 and problem 8, Ch5.