The main objective of this book is to provide the basic positions of sports analysis of contemporary fashion, and pave the way to settle the gap between the real priorities of the analysis, and the renewed reference to the free book from some key positions, comes in the forefront Allamenthia chains, and complementarities multiplier, and analysis on the real function. IR One of the hallmarks of this book is the lack of any form of engineering, this book consists of eight chapters. Chapter I: groups, relationships and Aldaol Chapter II real numbers and Chapter III Topouloggio metric spaces and Chapter IV Finishes Fifth Aldaol continuing metric space to another and sixth Aldaol real ongoing metric space, VII and VIII Integrating differentiation.