Finding a good area to study in analysis

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I'm an undergrad student and currently finding a topic for my thesis. Can I ask for help or suggestions on what area or part in analysis is good to study?

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I would suggest something in Functional Analysis, since it has many usefull applications. To get a first impression you can look at the book functional analysis and further topocs in analysis by Stein and Shakarchi. The book includes also an introduction to brownian motion and Fourier analysis. Maybe this is also something for you.