This book summarizes the main scientific achievements of the blown-up theory of evolution science, which was first seen in published form in 1994. It explores - using the viewpoint and methodology of the blown-up theory - possible generalizations of Newtonian particle mechanics and computational schemes, developed on Newton's and Leibniz's calculus, as well as the scientific systems and the corresponding epistemological propositions, introduced and polished in the past three hundred years.The authors briefly explain the fundamental concepts, then analyze a series of topics and problems of the current, active research widely carried out in the natural sciences. Along the lines of the analyses, they introduce new points of view and the corresponding methods. Also, they point out that the blown-up theory originated from the idea of mutual slavings of materials' structures so that numbers are transformed into forms . This discovery reveals that nonlinearity is not a problem solvable in the first-push system, and that the materials' property of rotation is not only an epistemology but also a methodology. The authors then point to the fact that nonlinearity is a second stir of mutual slavings of materials.