Reading has been one of my (many) hobbies for several years now. I’ve read hundreds of books but I won’t get tired. It’s a perfect way to both learn and have a fun. I like a variety of genres, but obviously mathematical non-fiction is amongst my favourites.
In the past two years, I’ve read dozens of maths books and loved most of them. I’ll keep reading them -I’m currently reading Things to make and do in the 4th dimension, by Matt Parker-, though lately I don’t enjoy maths books as much as I used. That is because some are very similar and after reading much it’s hard to come across something really original.
^Some of the books I’ll write about. These ones are Spanish editions, because my parents read them also!^
Here are my recommendations…
Non-fiction:
- Fermat Last Theorem, by Simon Sighn. This is a fantastic and engaging read, which I mentioned in my Personal Statement*. It is great for everyone, even for those not doing maths -my literature teacher loved it!-.
- The Code Book, also by Sighn. This book is not exactly about maths, but I found it amazing, really interesting. Truly recommended.
- Letters to a Young Mathematician, by Ian Stewart. This books gives a fantastic insight into how life is in the world of mathematics. If you are not a mathematician then 17 Equations that changed the world is probably a better choice, but anything by Stewart is good.
- Very Short Introductions, by Oxford U.P.. I won’t list them, it’s better to see the picture. Half a dozen are Mathematics; the other six, Physics.
They are all very good reads and quite easy to understand. If you happen to enjoy Fractals; then, The Fractal Objects (also in my PS*), by Benoit Mandelbrot, is awesome and was a cutting edge work when published. Of course, it’s harder to understand. - How not to be wrong: The power of mathematical thinking, by Jordan Ellenberg. Its former title, The hidden maths of everyday life, was a good enough description; but trust me, it is an enjoyable read.
Fiction:
- The Parrot’s Theorem, by Denis Guedj. A great intriguing novel. You do not need to know any maths to read it, yet you will learn some about the history of maths.
- Flatland: A Romance of Many Dimensions, by Edwin A. Abbott. Published in 1884, it is a very original masterpiece, set in a 2-dimensional world, which will make you question lots of things. I also used Flatland in my PS* (and was asked about it at my Cambridge interview!)
*A Personal Statement (PS) is a 4,000-characters essay required to apply to UK universities. It must explain why you want to study the degree you’re applying to, and why universities should choose you (over other students). Check out My Personal Statement!
I’ve tried to keep it short, but just ask for more books if you wish 🙂
I’d appreciate any reading suggestion. If you have a good one, please, comment down below!
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Maria A. Gutierrez 
You could read the book “How to think like a mathematician”.
Also you may find it https://scoutmathematics.wordpress.com/mathematicalresources/ interesting.
I believe that book was suggested on my reading list for last summer, and I found it similar to my first year courses, so although it would have been great at the time it wouldn’t be that useful now that I’m almost one third done with my degree. Thank you anyways!
OK, actually when I read it for the first time in 2016 I was still a high school student and I liked it a lot. But yes you are correct in saying that it only introduces us to mathematical thinking at a preliminary level.
You could read The story of Phi the world’s most astonishing number (I thought of recommending it in the first go but didn’t).
By the way if you want specific recommendations (in the sense that you say a topic like “Fibonacci numbers” or something) you can drop the topic names as a comment.
Also there are some really wonderful books written by author Raymond Smullyan (usually involves discussing rigorous things in a very pleasant and fun way) and some of them happen to be my favourites.