Thanks for the typo correction. I did just look it up but the book broadly speaks about REM & NREM in Chapter 3: An Infant Revelation — Two Types. And I am quoting the book here:

"NREM sleep received further dissection in the years thereafter, being subdivided into four separate stages, unimaginatively named NREM stages 1 to 4 (we sleep researchers are a creative bunch), increasing in their depth. Stages 3 and 4 are therefore the deepest stages of NREM sleep you experience, with “depth” being defined as the increasing difficulty required to wake an individual out of NREM stages 3 and 4, compared with NREM stages 1 or 2."

I would like to learn what is the fourth stage you are speaking of. I may have missed it somehow. Can you suggest me the chapter number?