Around the world there are many aspects of mathematical methods used to conquer problems associated with numbers which differ along with its theories to this book. The contents of this book are mainly first to book fundamentally and theoretical. The mission of this book is not the same as other books because it does not use as a constant at any form. Hence the theorems of the book are mainly first to be published within the history of mathematics. The life of mathematics is not complex nor difficult but as easy as possible. Dont Use the theory contant within this book . Use Leibniz notation. Try expanding this theorems with guessed theories In conclusion this book is theoretical and not practical. And it covers CALCULUS only. Important notes regarding this book Dear learner At the end of the book of study you should know The basics of calculus and its theories. Some arguments posed by this field. Possibilities of accuracy and proximities. Philosophies of mathematics and its infinity With such skills and knowledge . we then say welcome to the controversies of mathematics and science. The book covers the following subjects of mathematics Contents Algebra History Division of a polynomial Functions One to one function Many to one function Trigonometry Double angles definitions Calculus Gradient Tangent definition Algebraic calculus Trigonometric calculus Inverse functions within calculus Limits Exponential calculus Applications within calculus Exponential calculus Trigonometric calculus Advancement of analytical geometry and measurement The overall book entail partial calculus and the foundation of calculus.