An overview of analysis I'm looking for a book that gives an overview of analysis, a bit like Shafarevich's Basic Notions of Algebra but for analysis. The book I have in mind would give definitions, theorems, examples, and sometimes sketches of proofs. It would cover a broad swathe of analysis (real, complex, functional, differential equations) and discuss a range of applications (i.e. in physics and in prime numbers). I've looked at the Analysis I volume of the Encyclopaedia of Mathematical Sciences which Shafarevich's book is also a part of, but it focuses more on methods and isn't quite what I have in mind.
Thank you!

Loomis & Sternber's Advanced Calculus is available online.
It is a classic that goes well beyond what people normally call calculus
(differential equations, differential geometry, variational principles, ...).
Personally I really like Sternberg's books,
but it is a full blown textbook rather than a survey.
Or maybe Aleksander & Kolmogorov, Mathematics: Its Content, Methods and Meaning is closer to what you are looking for. It is more of a survey, but with a lot of depth. It is much broader than what you asked, but it is 1100+ pages and it is biased towards analysis related topics.
Another area to explore are advanced applied mathematics texts, these are often primarily analysis oriented, comprehensive and, well, application oriented and you can find books by people like Kreyszig, Lanczos, ... Dover have published a number of books like this.
