TITLE: Is there any wide sense but introductory Book series/websites for mathematics literature? (just to be familiar with)
QUESTION [6 upvotes]: Is there any Book/Book Series/Website which illustrate advanced mathematics but in concise and basic form. I just want to be familiar with the literature and I don't want a deep exploration of the topics. What I want is a near complete survey on different topics of math, What is important for me is the basic ideas and the connections between different parts of mathematics. For example if it talks about abstract algebra, then a quick survey of the concepts of group, ring,... and how these are connected to other topics...I just want to get a obscure grasp but pretty comprehensive topics.
BTW, I know there might not any reference but there might be a series of books. Or different book for different topics e.g. one of Geometric Algebra one for stochastic processing and so on. You know, I just want to get a good grasp of literature as a whole.
p.s. currently I'm interested in functional analysis, harmonic analysis, number thoery and operator theory.

REPLY [8 votes]: Luckily for you, one such book was compiled fairly recently: The Princeton Companion to Mathematics. 
The first part of the book contains an overview of modern pure mathematics which should allow you to hit the ground running. The third part contains a survey of 99 important mathematical concepts, and the fourth part contains longer surveys of 26 major branches of mathematics. There are copious cross references indicating how different branches and different concepts cross-pollinate. 
You can see the table of contents here yourself. 
Added later: actually, a second such book has also been compiled: The Princeton Companion to Applied Mathematics. It's of a similar layout to the "pure" Companion but covers very different topics. Some more information on the book, including a pdf of the table of contents, is provided at the linked webpage.