Has anybody read Khinchin's book on continued fractions by dover publications? It's like a fantasy book in my eyes. I can read it twice a year and still get excited every time in the grand finale! And it's all pure mathematics - he develops the theory of continued fractions with integral elements from null to diofanat equations, best rational approximations and he even proves great results in measure theory (the final result at least was proven by him) and I just love it.
However, I can't find any books like this one - which talks about the throry of a specific, rather small field and shows the developments in the field as a true storyline, and yet all rigorous and consistent, from null to advanced topocs. Besicovitch's book "almost periodic functions" is another fine example of the kind of books I look for. Does anyone have any suggestions for such books?
My mathematical maturity is of beginner masters degree, and I would like my reading to be challenging.
Thanks in advance, Or