One question would be what level of a student are you, and why are you reading this particular book? Based on an earlier question you've asked, you appear to be an experienced undergraduate or a beginning graduate student. So, what are you expecting/expected to learn from it? Further, how are you accustomed to learning?
Since the book does not provide exercises, I can well believe that the book is not a textbook, but rather a monograph ("a detailed written study of a single specialized subject or an aspect of it"). Not surprisingly, one uses a monograph differently from a textbook, and undergraduates rarely encounter monographs as a learning tool. So, you are correct to wonder just how to deal with it.
I would argue that monographs are written for researchers and are approached very differently than an undergraduate would approach a textbook. For an undergraduate class, the textbook is, in essence, the stuff you need to learn, and then demonstrate on an exam, and is written (mostly) by experts in how to teach the material to undergraduates. The exercises are the practice to help you learn the material and learn how to do the questions that will be on the test.
By contrast, the monograph is a whole bunch of detailed information presented by an expert in the field to present it all in one place to somebody new to the field but interested in becoming expert. There is no expectation that, by reading the book through once, you are suddenly an expert. There is no exam at the end of the ‘class’. Instead, the monograph is useful in several different ways, some of which only emerge over time.
So, how do I generally approach a monograph? Remember, I’m not an expert (yet), but am interested in the subject matter, likely because I see a need to understand it for my own research path. Maybe I will end up diving really deep, maybe not. First step is to look over the organization of the book – what does it actually cover, what order does it go in, are there technical (journal) references readily available in the text or as end notes. This step is to evaluate the relevance, and sometimes I don’t proceed from there. Now, in your case, the book was recommended to you, and if by your advisor the ‘recommendation’ is more than a suggestion.
Next, I read the first chapter. Often this is an overview of what the monograph covers, and I may have already skimmed it in my first step. But this is the time to pay a bit more attention. Is there jargon I don’t know, is the point of the monograph detailed, is the subject of the monograph placed in context of the field?
Assuming the first chapter is an overview, it is time to start into the meat of the monograph. But, I’m not reading for all the gory detail, but I’m also not just skimming it. What does the chapter cover, do I get the general idea, am I totally stumped? If totally stumped, then it is time to put the book down and go find a textbook with more basic stuff in it to review. If I’m getting the general idea, great, but may still choose to skip over more detailed parts for now. If that chapter goes well, I continue onward as long as things seem OK and interesting.
At the end of reading, I am not an expert. I do now know the areas that the monograph covers, and where in the book they are covered. Maybe I’ve looked up a few of the papers in the references. Maybe a section or two has really caught my eye as being directly applicable, and those I’ve probably read more carefully already. Am I done now? Perhaps, but it is time to evaluate what the next steps are, based on why I’m reading the book in the first place. Do I need to read more background material? Do I want to go and talk with somebody to clarify something? Did something really catch my eye? Evaluate where you are and what to do next.
Sometimes the book goes on my shelf and is not touched again. Sometimes it migrates to my desk since I keep referring to a specific section in it. Sometimes it gets pulled down a read through again, more thoroughly. It all depends on what your specific need is for the information.
This is, in the end, not all that different from how I approach journal articles. Something catches my eye and I download it. I’ll skim the abstract and the intro, glance at the experimental section and the figures, skim the final section. Often that is all and the paper gets filed away in case I need more info. Sometimes it gets read more carefully, sometimes I look up some references, sometimes I discard the paper.
Ultimately, as you transition to graduate work and research, you start learning differently. You start evaluating for yourself what you need to know, and how deeply. Frankly, it starts being a lot more fun. Good luck.