What math category would this solution fall under?

Question

Here is the word problem.

You are climbing a staircase. It takes n steps to reach the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

So for example, given 10 stairs, how many different ways could there be

What formula can be used to solve this problem?

Also, I would like to know two other things:

1. Category (ex. algebra, algebra II, etc.)
2. Any resources (books, lectures, etc) that I can use to educate myself in questions like this.