what levels of math are there?

If you are just talking about class names in the US, I would say they are: Algebra, Geometry (sometimes these two are reversed), Pre-calculus, Calculus 1, Calculus 2... then in college you might take any number of courses.. linear algebra, vector calculus, number theory.

Outside of a particular education system, I don't think it is helpful to think of math as "levels". There are all sorts of "areas" in math. Many of them don't depend on each other.

Algebra (which deals with functions, but there is a strong disagreement between educators as to what should be covered "algebra" in secondary school). There are also many subjects in the umbrella of Algebra. People study algebra all the way through graduate work in technical fields.

Geometry is the study of shapes and spaces. In high school geometry is used to study logic, but there is a lot more. There are subjects in geometry that are studies in your graduate work (or higher). Topology (a part of geometry) is pretty interesting.

There is Calculus, which is the study of how functions change and relate to each other.

Other areas of math are number theory, probability and statistics, game theory, graph theory... and many others.