This book contains valuable lessons of scientific value in mathematics, especially in relation to the wide field of sports (Algebra(.This book is the unique encyclopedia of mathematics that helps in the teaching profession and in the culture of mathematics and in the contemporary aspects of this book with the various sciences of physics, engineering and technical sciences.Since childhood I got accustomed to study with a pen in my hand.I extracted theorems and formulas, together with the definitions, from my text books.It was easier, later, for me, to prepare for the tests, especially for the final exams at the end of the semester.I kept (and still do today) small notebooks where I collected not only mathematical but any idea I read in various domains.Besides the textbooks I added information I collected from various mathematical books of solved problems I was studying at that time.This book contines the following chapters which are: Arithmetic, Plane Geometry, and Space Geometry, Algebra (9th to 12th grades), Trigonometry and Field and Galois theory.The researcher Mr. Nouh Hassan has relied on special curricula for educational education, research education and mathematics. It is a riches for the pioneers of mathematics and the world of the comprehensive scientific level.Author Nouh Hassan17/11/2019