This document summarizes key ideas from Gottfried Leibniz's contributions to calculus and provides examples of how to solve calculus problems involving velocity, acceleration, integration, and area under a curve. It also explores calculating volumes of revolution and costs associated with gold rings. The summary explores Leibniz's notation of dx and dy, how he viewed variables as sequences, and how his approach generalized calculus to multiple variables. Examples are provided to demonstrate calculating distances, speeds, and areas using graphs and integration.