He is known for three of his books on mathematical analysis: Functional Analysis, Principles of Mathematical Analysis, and Real and Complex Analysis. The second and third books are affectionately called Baby Rudin and Big Rudin (or sometimes Papa Rudin) by math students.
Rudin was born into a Jewish family in Austria in 1921. They fled to France after the Anschluss in 1938. When France surrendered to Germany in 1940, Rudin fled to England and served in the British navy for the rest of the war. After the war he left for the United States, and earned his Ph.D. from Duke University in North Carolina in 1949. After that he was a C.L.E. Moore Instructor at MIT before becoming a professor at the University of Wisconsin–Madison.