The book takes an engineering approach to understanding mathematics. That is, we view numbers as a tool for solving practical problems, such as characterizing the size of a collection of objects. The tasks that numbers help us with are expanded as one realizes that one can generalize our initial idea of what numbers are to solve more general problems.
Thus we start with the natural numbers, such as 1, 2, 3, etc., defining their properties and deducing consequences of these properties. Then we generalize the natural numbers to the integers. The integers include the natural numbers, the negative numbers, and zero.
The integers can be generalize to include fractions, or rational numbers, and these in turn can be generalized to the real numbers. Finally, the real numbers can be generalize to the complex numbers, which include a number whose square is negative.
The complex numbers are likely to be the most sophisticated numbers students have met in high school. Furthermore, while the natural numbers, integers and fractions can be fairly well understood without formal rigorous study, the real numbers and the complex numbers have properties that are not initially intuitively obvious.
These properties are probably not of interest to people not interested in a career in a technical field. But they can be of considerable interest to those who are, even if they don't want to study mathematics more formally. In addition, if they next begin a university education in science or engineering, they may find additional material and alternate approaches to these topics in high school would have been useful.
For example, complex numbers are used as a tool for solving many problems in differential equations. And the basic equation of quantum mechanics involves complex numbers, even though it is not obvious how a number whose square is negative is related to any physical quantity.