How can I advance? Right now I am 13. I have studied at the normal pace at my school, however, since this academic year I have felt that the pace the classes move at are too slow and I wish to advance faster. I would like to know how I can advance in maths and whether I should be advancing or staying at the set pace of my class?
 A: In today's world there's so much you can find online or at the library (local/community college/research institute). Continue to take math classes at school as there's value in group learning and having a teacher to answer questions, but by all means continue to push yourself and learn more. If you have an approachable math teacher, you might want to talk with them to gain further insights on what you should do next.
Online Sources
I would suggest to look to online sources such as Khan Academy. There they provide videos where you can touch up on things you have learned (perhaps algebra and arithmetic) and continue to learn more such as pre-calculus and on. The videos go up thru calculus, differential equations and linear algebra, which can be the equivalent of the first two years of undergrad.
This site can be a great learning tool. Ask questions and see if there's any you can answer. You'll learn a lot by just browsing around here.
Read math blogs or watch math videos on YouTube. [Note: These are generally not rigorous learning sources for independent study, but imo they help peak curiosity and are just cool] Some of my favorites are Numberphile, Mathologer, and 3Blue1Brown who all provide very interesting and fun examples and inquiries into math.
Books
Under the [reference-request] tag here on this site you can find several books and articles in a large variety of subjects that may be of interest to you.
A: You definitely want to advance if you can. The syllabus used in class is supposed to accommodate your average student, so if you want to be good or exceptional at maths you will have to put in work yourself.
The first thing I recommend to do is to talk to your teacher and make sure you and him are on the same page. That means he might try to stretch you more and not give you just what the rest of the class receives. 
Secondly, do not cover material which you will cover later on in school. A prime example of this is calculus. Calculus will make up a big chunk of your maths education at school when you are 16/17/18 years old. Don't spoil the fun of learning about it then by covering now, otherwise classes will seem even more easy and as a result boring. 
Stemming from the last point, at your age Olympiads are the natural path to go for. Once you become relatively good at them, they are great fun, especially if you become seriously good at them and get to travel to exotic places for things like the IMO. I personally enjoyed working through the 'Art of Problem Solving' series and from there working through Olympiads from around the world. Once you acquire a basic arsenal of mathematical weapons you can enquire into other books which might specialise into Number Theory, Geometry etc. 
I hope this answers your question. If you have any follow up queries just comment down below. 
A: I found this book incredibly useful. Actual textbooks on more advanced mathematics, at your age, can feel incredibly dense and abstract from the kind of problems you're interested in. I prefer to learn by solving problems, and this book neatly combines problem solving with an introduction to formal mathematical reasoning (like proofs by induction, and by contradiction). There's also a newer version which includes more geometry! 
If you want more recommendations, feel free to ask, but my fundamental advice is: go at your own pace, and don't feel compelled to try to hit advanced material at age 13. If you like solving problems, solve problems - don't feel compelled to learn calculus "because you should be doing that." You'll get there on your own one way or another - but if you go at your own pace, you'll enjoy it more.
