This monograph presents an interpretive essay on the foundations of Leibniz calculus, accompanied by key texts in English translation. The essay examines Leibnizs evolving views on infinitesimals and infinite numbers, tracing their development from his early metaphysical ideas to his mature justifications of the calculus. Leibniz first proposed treating infinitesimals as fictions in the 1670s, in line with the mathematical practices of his time, where abstract concepts could be used in calculations without implying their existence. By 1676, he rejected their status as quantities, yet continued to refine his arguments on this topic into the 1690s. The essay concludes with an analysis of Leibniz defense of his calculus in the early 18th century, showing how his later works naturally extended from earlier insights. This monograph will be a valuable resource for scholars and students of Leibniz and the history of science.