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I'm really enjoying the AMS column "What is ..." (http://arminstraub.com/math/what-is-column) and The Princeton Companion to Mathematics.

I am looking for something similar. I'd like to acquire some intuition behind different subjects and the general overview rather than digging into details and technical proofs.

I want to read more about the motivation, the greatest results and applications (inside and outside of mathematics).

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    $\begingroup$ As previous vague and broad big-list questions, this will soon be closed, then reopened, then closed again, then reopened again, ... for some random outcome. $\endgroup$
    – YCor
    Commented Jun 12, 2018 at 15:53
  • $\begingroup$ I read through the Bulletin of the AMS, which is a mix of feature articles and book reviews. It's higher level than is ideal for your purposes, but it has given me some idea what's happening in different areas. $\endgroup$
    – arsmath
    Commented Jun 12, 2018 at 17:23
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    $\begingroup$ I'll be interested in any answer to this question, but I do think it's far too broad for this specific site. $\endgroup$
    – Noah Schweber
    Commented Jun 12, 2018 at 18:04
  • $\begingroup$ "The Princeton Companion to Mathematics" might be a good source for some such material. $\endgroup$
    – Michael Greinecker
    Commented Jun 13, 2018 at 2:48

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On the popular level, there is an AMS feature column: http://www.ams.org/samplings/feature-column/fc-current.cgi and a series of 10 volumes "What's happening in mathematical sciences": https://bookstore.ams.org/HAPPENING, also by AMS.

On a higher level, there are journals which publish surveys, addressed to the general audience of mathematicians: Bulletin of the AMS, Russian Math Surveys, Sugaku expositions, Gazette des Mathematiciens, Expositiones Mathematicae, L’Enseignement Mathématique, and several other such journals.

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An addendum to Alexandre's answer: I have noticed that in some "proceedings" or "conference" volumes, the first article (or the introduction) is a very nice overview of the theory that is treated in the book. The same can be found in books with the title "on the occasion of the [age]-th birthday of [some big name in mathematics]".

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Look for books with the word "Handbook" in the title. These often contain well-written survey articles by leading experts. The downside is that "Handbooks" tend to be rather expensive, but you may be able to find them in your library.

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