In need of book recommendations (Soft Question) I tried to label this with as many soft question labels as possible to avoid immediate downvotes.
To give you a gauge of where I am math-wise, I'm a senior in high school who has gone through all the basic subjects (geometry, algebra, trigonometry, basic statistics/probability, calculus I). In addition, I've explored a few more advanced concepts on my own (mostly pertaining to calculus).
For the holidays, I told my parents that I'd like some solid math books in more advanced subjects so that I can further my knowledge, but local bookstores don't have anything of that calibre. 
My question to you is to give me great recommendations for books on more advanced topics I'd like to begin studying (the two I listed are complex analysis and number theory). However, I'm more than open to books that will go further into geometry, trig, algebra, or calculus if they are worth the read in your mind. Additionally, books in other subjects that would give me a good start in new areas of math are completely fine. I enjoy being challenged a great deal and have yet to fail to grasp any area I've studied thus far, so don't hold back unless the book pertains to material that requires calc III, for example.
If you need any additional information, just ask. Again, sorry for the soft question.
 A: If I were you, I would just watch some videos from the MIT Open Course. At the beginning it's really really much easier if someone is teaching you mathematics instead of reading by yourself. Expecially first year subjects. Take a look and pick a course:
http://ocw.mit.edu/courses/audio-video-courses/#mathematics
If you're more interested in Physics I would definitely watch Susskind lectures which are perfect for highschool students or first year college.
This is to build something you will find in the future, if you're just in need for something fun without any real effort I can suggest you: "Goedel Escher and Bach" by Hoffstadter, "Indra's Pearls" Mumford, "Road to reality" of Penrose... or whatever divulgative book you prefer, but I'm not a real fun of this way of proceeding: you never really quite get something you can really use from divulgative books.
A: Regarding number theory:
I'm a high school junior and read Number Theory by George Andrews sophomore year. I found it very inspiring with its survey of number theory with a combinatorial approach. Topics include the fundamental theorem of arithmetic, modular arithmetic, arithmetic functions, partition theory, and generation functions. Its introduction is very accessible, reviewing things like induction and assuming no previous knowledge of number theory. However, don't be fooled; it requires lots of work and has plentiful exercises ranging from easy to very difficult (for me, anyway). A free copy of this book is available online.
A: Springer's Undergraduate Texts in Mathematics are a great series, that range through the undergraduate curriculum. They are always the first book I look for while browsing the bookshelf of my university library. I suggest you do the same (go to a nearby university, the libraries are open access), and look for the Springer's « UTM » books.
Hartshorne's Geometry: Euclid and Beyond is a great book about geometry that will walk you through Euclid's Elements in the first chapter, and then introduce you to the axiomatic method and more advanced subject. There are many interesting and challenging exercices.
As for complex analysis, I suggest a book that will present the geometric aspect of the subject. You might also need to do some rigorous real analysis beforehand, as this might be a prerequisite for some books. For that, I strongly recomand the great book Understanding Analysis from Stephen Abbott. It will teach you rigorous analysis alongside a good intuition, and a stimulating problem driven presentation (not to mention the interesting exercices).
A: A Primer of Real Functions, Ralph Boas, either the original edition (small pocket hardcover) used, or the current, updated edition (ppbck), which has added material by (I think) his son (another Boas). It's not intended as a textbook, but rather as an introduction to modern analysis, aimed at students who, like you, have completed a standard curriculum through calculus (single variable at least) and are interested in bigger picture and ready for greater abstraction. (***** — 5 stars)
Here's a link to the official MAA page for the current edition: http://www.maa.org/press/ebooks/a-primer-of-real-functions.
A: A rather nice read is Stillwell's The Four Pillars of Geometry. First of all, it's quite readable, novel-like really. It's not dense, so look elsewhere for a rigorous, axiomatic or abstract text. The text serves as a sort of foray into geometry. The book has eight chapters and each one is a taste of different ideas.
The "Four Pillars" are the axiomatic approach (Euclid), vector geometry, projective geometry, and transformations. The last chapter on non-Euclidean geometry is a very fun read, too. I like this text, as it gives you a strong skillset, is a quick read, and gets the reader excited about differing subsets of geometry. And if I recall correctly, each chapter gives references to more advanced textbooks to further your studies.
A: I recommend The Princeton Companion to Mathematics and The Princeton Companion to Applied Mathematics.


A: Tristan Needham's Visual Complex Analysis is fun
https://books.google.com/books?id=ogz5FjmiqlQC
