Question: I came across a really interesting thread in the Internet where the author was asking for fun, but serious Maths book recommendations. I saw plenty of excellent books being recommended there and thought I'd start a similar thread over here :)

Some characteristics the books should have

1. They should be readable and friendly.
2. They should be dealing with topics that are not commonly taught at the school or undergraduate level.

I don't want books dealing with very commonly taught topics like differential equations, or Calculus by Spivak, which though elegant is not what I'm looking for.

Here are some examples of books I liked to make myself clearer: 

1. **Visual Complex Analysis *by Tristan Needham*** - I like this book for the simplicity and the sheer beauty of it all.
2. **Cauchy-Scwhartz Inequalities *by Micheal Steele*** - Mathematical inequalities are not a very advanced topic, yes. But, it's also not taught extensively.the author describes this book as a master class where mathematicians come to fine tune their skills, and that's exactly what it is. I loved it.
3. **Concrete Mathematics *by Graham Knuth and Patashnik*** - Again a very readable book. It doesn't deal with mathematics that is very advanced, but then again it gives a very beautiful and new treatment to it.

	4. **Flatterland \_ Ian Stewart** A wonderfully readable book.

I hope this gives you a clear idea. If you have any questions regarding what I'm looking for, you could ask in addition to your recommendations. I don't mind books on problem solving and the history of mathematics too.

Answer: 
School level:

1. Intuitive Topology, V. V. Prosolov.
2. Stories about Maxima and Minima, V. M. Tikhomirov.
3. Mathematics can be Fun, Y. Perelman.
4. What is Mathematics?, Courant and Robbins.

College:

1. Proofs from the Book, Aigner and Ziegler.
2. On Numbers and Games, Conway.
3. The sensual (Quadratic) Form, Conway.

General:

1. A Mathematician's Apology, G. Hardy.
2. Logicomix: An Epic Search for Truth, A. Doxiadis.
[Cited several times](https://www.google.com/search?q=site%3Amath.stackexchange.com+%22street+fighting%22) on Math.SX, [*Street-Fighting Mathematics*](https://mitpress.mit.edu/books/street-fighting-mathematics), by Sanjoy Mahajan, can be an example of *fun but serious Maths book*.