As the commenters already argued, I would not regard this book as a self-contained introduction. For instance, from a brief browse through the introductory chapters:
The reader is assumed to be familiar with CW-complexes and several of the major theorems about them already which will be generalized (e.g. the Whitehead theorem).
The reader is assumed to be familiar with homotopy in the classical sense (e.g. they point out that "homotopy" isn't an equivalence relation on maps of simplicial sets as an implicit contrast to the case of spaces).
The reader is assumed to be familiar with other important tools: e.g. they say "Recall that the integral singular homology groups $H_*(X;\Bbb Z)$ of the space $X$ are defined to be ..." (this is on page 5) and they assume structural properties of it are known.
They describe the geometric realization of a simplicial set as
$$
|X| = \varinjlim_{(\Delta^n \to X)\text{ in }\Delta \downarrow X} |\Delta^n|
$$
which is certainly concise and categorically valid, but assumes that the reader already has some familiarity with the point of this construction and some of its basic properties. For example, more introductory references would discuss how each point of the realization is in the interior of exactly one n-cell, give a proof that the result is a CW-complex, etc.
Simplicial sets are a fundamental tool used basically everywhere in modern homotopy theory. However, the reason for this is that there are concrete technical problems which they solve. I realize that it might be tempting to try to skip ahead to get to the more advanced material, but it can be very difficult for a student to "get the point" without first understanding the more basic material.