The purpose of this book is to make available to the student some fundamentals of mathematical analysis. Specifically, it is intended to make such fundamentals available in a form that meets their need in many applications, like real analysis, integration, measure theory, and representation theory. The principal point of view is to develop the basic structures of analysis, under which one can appropriately go on further in the domain of functional analysis. The book is intended to be essentially self contained and accessible to well-trained under graduated students. Its prerequisites are elementary standards from basic algebra. In writing this book, we care about doing things as little abstract as possible. So, to make easy the access to the main concepts, each section of each chapter is illustrated by simple examples and exercises, which are mostly applications to concrete problems.