Very readable book. I'm not fully convinced by all of the arguments, but the book makes me avidly pursue those arguments.
The book involves various detailed discussions about mental causation, mind_body problem and the concept of reduction, generally. But I think the main line of the book is as follows:
Kim starts the book by asking the main question of his discussion: how physicalism could explain mental causation? Is it possible at all?
It seems very plausible and undeniable that mental causation is real. I decide to raise my hands and then I raise my hands. Thus, it should be presupposed in each solution to the mind_body problem. Kim, tries to formulates physicalism, and He distinguishes between two types of physicalism: non-reductive physicalism and reductive physicalism. Kim, then, in a long chapter (chapter 2) presents many arguments (almost all of them are based on supervenience thesis and the principle of physical causal closure) to show there is no way to reconcile between non-reductive physicalism and mental causation. Thus, Kim concludes that mental causation rules out non-reductive physicalism, and therefore the only view remains for us is reductive physicalism. But, is reduction of mental to physical is possible? Kim argues that the only plausible way to reduce mental to physical is functional analysis of mental (it's interesting to note that Kim not only deny functionalism [I think realizer functionalism] as a form of non-reductive physicalism, but also he thinks it's the only plausible form of reductive physicalism). But, does functionalization of mental in principle possible? It depends on possibility of functionalization of all mental phenomena: that is intentionality and qualia. Contrary to some philosophers such as John Searle and Hillary Putnam, Kim sees no difficulty in functional analysis of intentionality. He thinks the main difficulty is reduction of qualia. Kim thinks there is very good arguments against reducibility of qualia, such as possibility of inverted qualia.
So, Kim claims that mental causation leads us to decisively reject "middle of the road" positions like property dualism, anomalous monism and non-reductive physicalism. Also, he thinks substantive dualism seems out of menu (although he doesn't reject it). However, it seems he leaves unanswered the question of what should we do with phenomenal mental properties?