Question

how many axioms exist

Answer 1

There are infinite axioms in mathematics. They keep increasing in number every year. However, most of the axioms of Geometry were given by Euclid.

Answer 2

Axiom are many in numbers.

If we say that they are infinite then we are not incorrect.

Actually, axiom get forms on the basis of condition.

Like we can consider any two different things related to each other in quite many ways.