Non-textbook Math book recommendation to read to my kids I'm looking for a book to read to my kids.
NOT a kids book, but not too mature for a kid. My youngest kid that reads with me is 6 and the eldest is 10.
I'm looking for a book that is good literature, and is hard to put down. 
Also maybe a book that makes the subject in school more interesting. Not just tedious memorization, but presenting it in a way that makes the child excited about what he/she is learning. And not a book that teaches the subject, (math etc....) but a book that teaches how it got started or why it's important. 
Are there any books like these you that you have read that made you excited about math? If so please tell me.
 A: When I was a child, I really liked the book The Number Devil by Hans Magnus Enzensberger.
A: These two books by Apostolos Doxiadis, have been generally praised:


*

*Uncle Petros and Goldbach's Conjecture

*Logicomix (a graphic novel, aka a comic book)
I am not sure they are suitable for 6-10 year-olds, but then again the other suggestions I saw here aren't as well. So I thought I'd suggest them and you can decide if they are appropriate for your kids.
A: The Infinite Farm will turn your child into a budding set theorist. 
A: I really loved The I Hate Mathematics Book: it's whimsical, and genuinely funny, as it tackles math that's both interesting and accessible. 
It's been decades since I read it last, but I recall that it tends to focus on Discrete Math - my favorite type. 
I don't know if I loved the book because discrete math is somehow intrinsically interesting to me, or if I found discrete math so interesting because of the fond memories I associate with this book. 
Either way, I highly recommend it. 
A: Anything by Raymond Smullyan He always starts with wonderful logic problems about liars and truth-sayers, and uses that as a springboard to tackle very deep math (over your kids heads, but you do not need to go into that part of the books).
A: Richard E. Schwartz has found a new format for "Math books for kids", and they are delightful. Get You can count on Monsters, and Really big Numbers. The first is a favorite nighttime book for both my 4 and my 11 year olds.
A: Not really mathematics, but do check out Norton Juster's Phantom Tollbooth. It's surely  age appropriate; some of the other suggestions here are a stretch, I think.
A: It's not a textbook, but it's not really a storybook either.
I had utterly forgotten about it until I saw your question and started thinking. When I was a kid, I really liked reading a set of childrens' encyclopedias that we had. 
Thanks to Google, I think it was Childcraft Annual's Mathemagics.
From what I remember it was filled with short-story-type things illustrating various math and logic puzzles. I enjoyed reading and re-reading them and thinking through the logic puzzles.
This website has a review of the book and a few photos.
Two relevant quotes from there:

Mathemagic is laid out brilliantly. It baits the hook by opening with things kids love – puzzles, tricks and games. The first chapter, if read sequentially, takes readers by the hand and welcomes them into the world of math, logic, and the beauty of rational thought.
Because we read through Mathemagic as an evolving story, we noticed how each chapter got a little richer, a little more mathematical, but always practical, vibrant, and accessible. After puzzles and riddles, we got the history of numbers, counting, and math.

I'll also mention "Lockhart's Lament", not as something to read to your kids, but as something that is a good read for anyone interested in math. It illustrates how the "math" that is taught in schools really eliminates all that is fun in math: thinking, puzzling and coming up with solutions. Although, based on you asking this, I suspect that you probably already know that ;)
A: Definitely
https://en.wikipedia.org/wiki/The_Number_Devil
by Hans Magnus Enzensberger
In Italy the title is "Il Mago dei Numeri" (The Numbers Wizard) to avoid offense to Vatican Holy See Pope, I guess :)
The original title is 

Der Zahlenteufel. Ein Kopfkissenbuch für alle, die Angst vor der
  Mathematik haben

More or less 
The number devil. A pillow book for those who are afraid of mathematics
A: Scour the web for copies of any book you can find by Yakov Perelman. The titles vary because of different translators, but he is absolutely lovely.
Recreational Physics for instance, illustrates basic physical phenomena with everyday stories and excerpts from famous books (Jules Verne) was a favorite of his. It is not math, but such a glorious read, aimed at youngsters.
I had Recreational Mathematics and Recreational Algebra too, and they were two of my favorite books ever.
A: I would strongly recommend these : 


*

*Puzzles to Puzzle You from an Indian author, Shakuntala Devi and

*More puzzles to puzzle you from the same. These two induced a zeal of Puzzles in me and made puzzling dear to my heart. Mathematics was already loved by me, but hitting the dopamine with puzzles is a feeling of a different level.  


Currently, I am reading these two books:


*

*My Best Mathematical and Logic Puzzles from Martin Gardner.

*To Mock a Mockingbird by Raymond Smullyan
A: It's a bit of a long shot given your question, but it's so good I think it would be a pity not to mention it: The Neverending Story [warning: TVTropes link, do what you want] is infused with a certain fascination for philosophy, logic and paradoxes.
Never pedantic, intimately scholarly, reads like a thriller, ages 6 to 106.
If I remember correctly, the book introduces, among others, several classical paradoxes, the infinite monkey theorem, the notion of self-similarity and of decision trees to a wholly unsuspecting reader.
I also seem to remember that, at some point, the Ivory Tower is characterized in a geometrically interesting way as being equidistant from all other points in the land of Fantasia.
A: If you can tolerate some deviation from the posted specs (comp sci
rather than more general math, written for kids but accessible to adults
as well), I would recommend Lauren Ipsum: A Story About Computer
Science and Other Improbable Things by Carlos Bueno. It introduces many
computer science concepts in a witty and memorable way, and is a very
fun read. Kirkus review.
A: The World of Mathematics, edited by James R. Newman, 1956. I received this 4-volume set at the age of 10 as a gift, and although some of it was over my head, much of it was fully accessible to a youngster. In the 55 years since I first met this book, I've returned to it again and again. Unlike this reviewer, the book never gets old.
A: A couple of recommendations:


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*Abbott, Edwin Abbott, Flatland. A romance of many dimensions. With a new introduction by Thomas Banchoff, Princeton Science Library. Princeton, NJ: Princeton University Press (ISBN 0-691-12366-7/pbk). xxxi, 103 p. (2005). ZBL1088.00001. (The social satire is a bit dated, but the mathematical intuition is timeless.)

*Ivar Ekeland and John O'Brien (illustrator).  The Cat in Numberland. Goodreads link (My six year old loves this one.)

*Malba Tahan. The Man Who Counted: A collection of mathematical adventures Goodreads link

*Lockhart, Paul, Measurement, Cambridge, MA: The Belknap Press of Harvard University Press (ISBN 978-0-674-05755-5/hbk; 978-0-674-06734-9/ebook). 407 p. (2012). ZBL1259.97008. (This one may need to wait a couple of years, but positively oozes enthusiasm.)

A: A 1959 27-minute cartoon called Donald in Mathmagic Land https://youtu.be/AJgkaU08VvY is a cartoon, not a book, but I remember owning a comic book of the same name.  (The full bibliographic citation for the comic books is Walt Disney's Donald In Mathmagic Land, No. 1051, Dell Publishing Co., August 1959.)  Carl Barks was the principal artist associated with the comic-book version of Donald Duck.  The definitive source on Disney comics—https://coa.inducks.org—explicitly credits the Donald in Mathmagic Land comic book to writer Don R. Christensen, penciler Tony Strobl, and inker Steve Steere.  It can be bought on Amazon at https://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Dstripbooks&field-keywords=Walt+Disney%27s+Donald+In+Mathmagic+Land 
The cartoon received a 1959 Academy Award nomination for Best Documentary - Short. 
A: I liked Lancelot Hogben's Mathematics in the Making when I was a kid.
A: Things to Make And Do in the Fourth Dimension by Matt Parker is a fun read.
A: I received Puzzling Adventures by Dennis E Shasha as a gift in eight grade and thoroughly enjoyed it - I still have my copy on my bookshelf today. The book consists of a collection of mathematical puzzles connected by a fascinating cast of characters, including the inimitable Dr. Ecco, and contains an encrypted meta-puzzle that took me several years to solve.
A: Computational Fairy Tales by Jeremy Kubica is supposed to be good - it's more focused on computer science but I think is otherwise exactly what you're asking for.
A: Personally, I loved to read the Murderous Maths series by Kjartan Poskitt when I was younger. 
Each book talks about a certain area of maths, ranging from simple topics (such as arithmetic) to more complex (algebra, trigenomety). 
All the books use an ongoing story, recurring characters and humourous comics to explain both mathematics theory and history, as well as practical uses for these mathematical skills. They really do make learning the maths fun.
A: It has been a really long time since I read it so my memories about it are a bit foggy but I remember that I really liked The Parrot's Theorem by Denis Guedj. It is a fiction book that talks a lot about the history of mathematics.
The original version was in French and called Le Théorème du Perroquet.
Note that this may be a bit too complicated for 10 years old. Have a look and make up your mind for yourself but you may have to wait a couple of years.
A: I'm a big fan of the books of William Dunham, in particular "The Mathematical Universe" - https://www.amazon.com/Mathematical-Universe-Alphabetical-Problems-Personalities/dp/0471176613.
It presents actual mathematics, while maintaining an approachable, storytelling perspective.
His other books include Journey Through Genius, The Calculus Gallery, and Euler: The Master of Us All, though they're somewhat more advanced.
A: Try Nets, Puzzles and Postmen: An Exploration of Mathematical Connections! It is aimed at a lay audience but is extremely interesting even for a mathematically trained reader. I learned a simple proof of a complicated theorem from it (which was briefly sketched in a kind of endnote for more advanced readers)!
A: You could look at How to fold it by Joseph O'Rourke:
https://www.amazon.com/How-Fold-Mathematics-Linkages-Polyhedra/dp/0521145473
(This might be a little advanced, but not by much. And the geometry/handicraft aspect is fun even if you don't fully grasp the mathematics of it.)
A: *

*I am not sure whether someone already mentioned the relevant question having great suggestions:
Good math bed-time stories for children?

*Also, please have a look here (from someone who loves math books):
http://www.proofschool.org/math-books/

*Finally, here is one more great collection: http://mashupmath.com/blog/2017/5/5/13-stem-fiction-books-your-kids-will-actually-enjoy-reading-this-summer
A: I don't know if it's suitable for under 10 since I've only browsed through it a little, but my girlfriend really liked this one: The Simpsons and their Mathematical Secrets, by Simon Singh
https://www.simonsingh.net/Simpsons_Mathematics/
A: The Joy of X by Steven Strogatz.
A: The book Math Curse, by Jon Scieszka and Lane Smith link was a personal favorite. 
A: Fermat's last theorem by Simon Singh is, as you say, "NOT a kids book". Whether it's "too mature for a kid" depends on what you mean. Some of the mathematics may be too advanced, but don't sell your kids short. They will probably still be able to appreciate the eponymous problem (at least if they're interested in math in any way), as well as problems like the bridges of Königsberg and the 14-15 sliding puzzle. And, of course, the actual history that the book details. I remember having read and enjoyed (parts of) the book long before I was 10.
A: Arranged in decreasing order of approachability, here are some of my favorites:


*

*The Colossal Book of Mathematics - Discussion on several pop math topics

*Infinity and The Mind - A discussion about Infinity

*Gödel, Escher, Bach - About Intelligence, Symmetry, Self-Reference, etc

*Indra's Pearls - An interesting exploration in fractals

