Arithmetic is the heart of useful mathematics. Most people learn the many basic notions and computations of arithmetic on their own. As it gets more complex, there are techniques that one can learn to make it quite easy. Unfortunately, such techniques are rarely taught and tedious, backward techniques are taught instead.
We will start with counting, followed by addition, multiplication, subtraction, division, and powers. Those chapters will focus on simply doing the computational aspects with an eye to understanding what is going on relative to some intuitive pictures. We conclude this part with an abstract walk into constructing the natural numbers, integers, and rational numbers. Ideally these constructions will give some of these numbers a more accessible feel, but it is safe to skip over the constructions.
One of the main reasons for readers to read this book is that the methodology of computing the operations, going from left to right, naturally leads to a more intuitive appreciation for estimating the size of numbers. When we are taught to look at the left to start our computations, we naturally start looking left. And that is where the most essential information lies.