Terence Tao–type books in other fields?

Vakil's notes on Algebraic Geometry http://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf are written in the same style. A nice contrast to the terse, traditional nature of the standard reference, Hartshorne https://www.springer.com/gp/book/9780387902449


I know the OP probably knows this but for undergraduates, there are Analysis I and Analysis II by Terence Tao which follow the exact same style as mentioned in the question. The book is self-sufficient and Tao provides all the necessary background needed to solve the exercises. Some sample chapters can be found freely here.


One such example, for functional analysis, is Lax's book, "Functional Analysis." It's a very-received and commonly-used textbook (see https://mathoverflow.net/questions/72419/a-good-book-of-functional-analysis), and it leaves many results to exercises as you read along, similar to Tao's style.

Another example, although to a lesser extent, is Abbott's introductory real analysis book "Understanding Analysis." This is a very good book with in-depth explanations and visuals. The author leaves plenty of results to exercises, and in some sections, has you construct many of the tools yourself through guided exercises (such as the sections on double sums and Fourier series).

An additional textbook that has lots of discussion and illustration, while leaving a fair amount of results to the reader, is John Lee's "Introduction to Smooth Manifolds," which is one of the standard texts on the subject for graduate students. Although Lee is more proactive in proving results than Tao in most of his books, I'd say this still fits the description, at though to a lesser extent.