An infinitesimal quantity is a numerical function or sequence that tends to zero. Infinitesimal calculus is a general concept for differential and integral calculi that form the basis of modern higher mathematics. The analysis of infinitesimals is undoubtedly the most powerful and effective means of studying nature ever created by scientists. The formation of this concept is associated with the names of brilliant mathematicians: Archimedes, Isaac Newton, Gottfried Wilhelm Leibniz, Augustin Louis Cauchy and Karl Weierstrass. This book deals with the analysis of the infinitesimal and its amazing history.