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I would like an up-to date book which lists results with perhaps a comment on how to prove it, as this one. I have gone through the algebra section partially and I am awed. It provides definitions, lists results and has occasional comments. I try to prove, make my own examples and connections and discover it as much myself before referring formal books. I would like to know if there are similar books which are updated and include more advanced areas of mathematics as well.

EDIT1: Thanks for the answers. I plan to give the other answerers bounties as well once I have higher reputation.

Edit2: Related question on MO "Books with a theorems as problems approach"

Edit3: Sorry this question keeps appearing on top. Please refer: meta post

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    So is there any updated equivalent.2011-05-01

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Not quite the same thing, but there are books for self-learning that are similar even if much restriced in scope. See for instance, A Pathway Into Number Theory.

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For Linear Algebra, Paul Halmos has written "The Linear Algebra Problem book" that comes pretty close to what you want. For topology, take a look at "Elementary Topology Problem Texbook" by Viro, et. al.

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Somewhat of a different flavor I believe (I did not read Carr), but I think the princeton companion to mathematics might be something you are interested in. It is one of my favorite books in mathematics. It has some long articles introducing different parts of mathematics in depth, with current results and aims for the future. Also many theorems are explained in laymens terms (a mathematical laymen, i.e. not an expert in that particular field) in an encyclopedian part of the book.

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For Combinatorics you might want to take a look at this book, whose author is also quite well known.

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    "This book" is *Combinatorial Problems and Exercises* by Laszlo Lovasz.2011-05-11