This book emphasizes reasons, explanations and economic examples, avoiding the method of "defining an axiom and a principle", although the author is fully aware of the importance of this method. This book is not intended to be the latest reference manual for researchers. As a result, some important themes are unfortunately left out. In addition, my focus is not to state the most common theorems and propositions, but to try to make the explanation of this book as simple as possible, to minimize the preconditions for reading this book, but still to bring readers close to the forefront of the current basic analytical tools of economics. Unfortunately, in economics, it often happens that even among those who have written about a problem, some people don't understand the analytical structure of the problem. Once this analytical structure is understood, it is usually easy to extend it to a more general situation. Therefore, when discussing economic issues, my focus is to clarify their analytical structure. Similarly, this book is not like a typical "engineering mathematics" textbook that emphasizes "how to do it", although such books are often useful, and this book tries to explain the "why" problem.

As far as the preparation knowledge of this book is concerned, the economic theory learned in the second and third grades of undergraduate course should provide readers with enough economic background to start learning this book. The basic theories of calculus and linear algebra (such as the law of matrix multiplication) for two or three semesters should provide readers with sufficient mathematical foundation. For the convenience of readers, Appendix A contains a brief introduction of linear algebra.