What mathematical "tool" did Newton develop that has been essential to advanced physics ever since?

The mathematical "tool" developed by Isaac Newton that has been essential to advanced physics ever since is Calculus.

Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities. It has two main branches - differential calculus and integral calculus. Both of these branches deal with the concept of a limit, which is the basis for calculus. Differential calculus is primarily concerned with the rates of change of functions, while integral calculus deals with the accumulation of quantities. In physics, calculus is essential for solving problems related to motion, optimization, and various other phenomena which involve continuous change. The principles of calculus have been widely used in fields such as engineering, economics, medicine, and other areas of science, making it a crucial mathematical tool for understanding and solving real-world problems.