Summing Up Infinitely Small is a fascinating and profound work written by eminent mathematician and educator, Professor Nathanson. This book will be a real discovery for anyone interested in mathematics, especially in the field of analysis and limit theory. Nathanson, known for his clear and accessible explanations of complex concepts, offers readers a unique opportunity to immerse themselves in the world of infinitesimal quantities and their applications in mathematics. The book covers a wide range of topics related to infinitesimal quantities, starting with their historical context and ending with modern methods of their use. Nathanson not only explains the theoretical foundations, but also demonstrates how these concepts find application in various fields of science and technology. Readers will be able to learn about how infinitely small quantities are related to boundaries, derivatives and integrals, as well as how they help in solving real-world problems. This work will be especially interesting to students, graduate students and teachers who study higher mathematics, as well as to anyone who seeks to deepen their knowledge in the field of mathematical analysis. The book is suitable for both beginners and more experienced readers who want to refresh their knowledge or look at familiar topics from a new perspective. Nathanson skillfully combines theory with practical examples, which makes the material accessible and understandable. The topics raised in the book concern not only mathematics, but also the philosophy of science. Nathanson asks important questions about the nature of infinity and how our perception of infinitesimals affects our understanding of the world around us. Readers will be able to reflect on how mathematics shapes our perception of reality and how it is used to solve practical problems in engineering, physics, and other sciences. Nathanson's style is clear and logical, making his books easy to read. He skillfully uses illustrations and examples to illustrate complex ideas, which allows readers to better absorb material. His other famous works, such as "