"From scratch" is relative. The acquisition of knowledge is incremental. When kids learn how to add and subtract in first grade, they are supposed to have learned how to count in kindergarten. Likewise, when you reach the intermediate level in physics, you are expected to have learned something at the introductory level. I quote from the preface of the book. Taylor is talking about the students whom he taught out of this book at his institution.
"##\dots~## Almost all of these students have taken a year of freshman physics, and so have at least a nodding acquaintance with Newton's laws, energy and momentum, simple harmonic motion, and so on. In this book I build on this nodding acquaintance to give a deeper understanding of these basic ideas, and then go on to develop more advanced topics, such as the Lagrangian and Hamiltonian formulations, the mechanics of noninertial frames, motion of rigid bodies, coupled oscillations, chaos theory and a few more."
As you can see, he is well aware that the users of his book have not mastered the material, yet they have the basics which he can then proceed to reinforce. For example, the first equation in the book is the position vector, $$\mathbf{r}=x\hat{\mathbf{x}}+y\hat{\mathbf{y}}+z\hat{\mathbf{z}}$$He assumes you have seen this before and does not explain the idea of a unit vector. However, he shows other ways to express unit vectors, such as ##~\{\hat{\mathbf{i}},~\hat{\mathbf{j}},~\hat{\mathbf{k}}\}~## and ##~\{\hat{\mathbf{e}}_1,~\hat{\mathbf{e}}_2,~\hat{\mathbf{e}}_3\}~## and then summarizes vector operations (addition, multiplication, dot and cross product). What he is saying here is "I assume that you have seen all this before and that you understand what I'm saying. However if you don't, then you have to figure it out and/or relearn it from somewhere else. He is not going to teach you the concepts of unit vectors, vector addition and multiplication because that's where he draws the line separating what constitutes "from scratch" and what doesn't.
I hope this helps.
