Chapter 1. Metric Spaces.- Chapter 2. Continuous functions on metric spaces.- Chapter 3. Uniform convergence.- Chapter 4. Power series.- Chapter 5. Fourier series.- Chapter 6. Several variable differential calculus.- Chapter 7. Lebesgue measure.- Chapter 8. Lebesgue integration.
Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as "the undisputed king of all mathematics blogs".