This is an excellent introduction to the issue of personal identity for the beginner, and it's a pretty good recap of the main issues for someone with more philosophical training who hasn't thought about this particular issue in a while. Perry's book manages to covers a lot of ground without getting bogged down in details, and the dialogue format makes it more engaging than your usual, textbook-format introduction to some philosophical question. Moreover, its compression makes it an excellent book to teach. Since the arguments are compressed and the bigger issues are usually just hinted at, there's a lot that can be said about the arguments presented in the book beyond what Perry comes right out and tells you.
What is the question of personal identity? Basically, it's the question of what makes a person one and the same person through time. I assume I'm very same person I was two days ago, two months ago, two years ago, two decades ago, etc. Given that I've changed a great deal over that period of time, how could this be? What is it about me that makes me the same as the guy who was sitting in class two days ago, the guy who was anticipating spring break two months ago, the guy who was entering grad school two years ago, the kid who was sitting in some kindergarten class two decades ago, etc.? There's been a lot of physical and psychological change over time, and yet I think I'm the very same person I was at those various times. How could that be?
Perry discusses three views here. The first view is a sort of dualism according to which personal identity is a matter of the identity of souls across time. If this view is correct, what makes me the same as those guys is that we share a common soul. The second view is a sort of physical view according to which personal identity is a matter of identity of bodies across time. If this view is correct, what makes me the same as those guys is that we share a common body. The final view is a sort of psychological continuity view according to which personal identity is a matter of having appropriately related psychological states through time. So what makes me part of the same person as those guys is that there is a normal process of psychological development from the kindergarten kid through the first-year grad student through the guy sitting in class two days ago and up to me right now.
And all of these views have problems that the interlocutors discuss. Some problems for the soul identity theorist: What is this soul, and how can we know about it? How can you account for the fact that we think persons are closely connected to their physical bodies? Some problems for the bodily identity theorist: How can you account for the fact that we seem to be able to imagine cases in which the same person switches bodies? How can you account for the apparent importance of issues of psychological continuity to our judgments about personal identity over time? How can you account for the fact that we seem able to figure out who we are simply through introspection? And some problems for the psychological continuity theorist: What exactly is the relevant kind of psychological continuity, and can it be defined in a non-circular manner (i.e. in a manner that doesn't assume facts about personal identity through time)? And if it reduces to a kind of similarity, couldn't I be psychologically continuous with lots of future (or past) people even though I can't be identical to lots of different future (or past) people?
Each of these objections is pressed against the respective views, and some attempt is made to defend them against these criticisms. Since Perry's aim is to present the issues and the kinds of considerations that are relevant in thinking about personal identity, there is no attempt to reach a final conclusion on the issues.
And Perry tries to bring out that this is a philosophical issue with an importance beyond philosophy. He does so by focusing on the implications of these various theories for the possibility of human immortality and for existence after bodily death. If the soul view is correct, it seems to secure the possibility of my existing after my bodily death. But there are worries here. First, there are worries about the independent plausibility of the soul view; and second, there are worries about whether the soul view can be spelled out in such a way that whatever survives my bodily death is something recognizable as me. If the bodily identity view is correct, then it seems I exist only when my body does and thus survival of bodily death is impossible. Consequently, the prospects for immortality depend on the prospects for the eternal existence of my body. The issues are somewhat more complicated with the psychological continuity view. It seems to be consistent with my surviving bodily death, as it seems there could be a being with psychological states continuous with mine but who doesn't have a body. But things aren't as clear as they may seem unless we know something more about just what sort of psychological continuity we're talking about. On some views, the relevant sort of continuity requires something like the causal relations between psychological states that occur within the human brain. And if that's what kind of psychological continuity would be required for me to exist beyond my death, it's not at all clear that this allows for the possibility of survival after bodily death.
I recommend this book for everyone interested in the question, and especially to those who are new to the subject. Perry both introduces the basics of the subject, and he presents variants on some classic and contemporary arguments in the literature. So the book also serves as an introduction to the literature on the subject. It would, of course, be helpful to supplement this book with Perry's collection on personal identity, which includes the classic work (by Locke, Butler, Reid, and Hume) on the subject and some of the most important recent work (by Shoemaker, Williams, Parfit, Nagel, et al).