This is a very interesting read on Penrose's new hypothesis: conformal cyclic cosmology. Before he gets to this in the third part of the book, he first needs to give the reader the background to his thinking. To that end, the first part of the book looks at the Second Law of Thermodymanics, which plays a pivotal role in this work. So if you don't yet have any idea what this is, I would recommend a little preliminary reading before tackling Cycles of Time.
If you are not familiar with Penrose's writings, then this perhaps is not the best starting point. He jumps straight into the Second Law and doesn't shy away from the necessary maths. For a science graduate, this is relatively easy reading, though those without a formal background in maths or physics may struggle, although Penrose's styles of diagrams are immensely helpful. One thing that is helpful is that even if you haven't grasped all the detail in a given section (and I certainly didn't) then that doesn't mean you cannot grasp any of the later concepts.
No one could ever accuse Penrose of patronising his audience, and though many topics will be familiar to scientists, Penrose's particular style always stretches you and makes you think in a slightly different way; so that which you thought you knew quite well suddenly has a few extra question marks posed against it. One thing that is very praiseworthy in this book is Penrose's modesty and his clearly laying out of what is well evidenced scientific consensus and what is his own minority view, as well as pointing out the drawbacks in his own theory. This style contrasts greatly with the brash optimism that Hawking & Mlodinow put forward in their book, The Grand Design, published within a few weeks of Cycles of Time. The fact that Penrose does this raises some interesting questions. For example, he does state that in order for his hypothesis to be correct, we would have abandon many well-established theories, such as the invariability of rest-masses of fundamental particles.
I could not claim to have fully understand all the nuances and detail of this book at the first, but that does not diminish my enjoyment of it or my ability to get the overall gist of it. I will be re-reading this book, going over each line in more detail in order to get the complete picture.