In writing this book I think it is likely to be of interest to those who are not satisfied with following a procedure without understanding it. For many people, what we know about numbers and arithmetic operations is enough to survive and perform within the demands of everyday life. However, It will be a great pleasure to explain rationaly and based in logical processes all that are the numbers we use today and especially why we do the arithmetic operations as we do them. Many of the reasonings and explanations used in this book have obtained through the author's reflections on how they could occur to the men of antiquity, certain solutions to problems of quantity management or the design of simple methods to perform arithmetic operations. In other cases, however, the concepts have been taken from books and publications written by experts in the history of mathematics and when that happens, the reference to where they come from is clearly especified.