What did Isaac Newton invent in mathematician?

Well, one major thing (and his most famous work) would be "Philosophiae Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy) which he published in 1687 with his friend Edmond Halley.

This showed how a universal force, gravity, applied to all objects in all parts of the universe.

He also was very interested in Fluxions (Calculus) but I don't know if he invented it.