David Harvey is actually a geographer, but from reading this book, one would think him one of the great political economists. Based on this work alone, he should be in the popular range of Stiglitz, Schumpeter, Milton Friedman etc., but it is not likely that such 'honor' will ever befall a Marxist theorist. Nevertheless everyone interested in Marxist economics, for whatever reasons, simply must read this book.
Harvey's discussion of capitalism from a Marxist perspective is extraordinary clear, sharp and thorough. So much in fact that it is probably the most consistently in-depth exposition of capitalism from every aspect since "Capital" itself. This also makes it hard to review it, since one hardly knows where to begin.
Fortunately for political economy newbies (and this book is definitely the best kind of "introductory overview" you could give to an intellectual person), Harvey starts at the same point "Capital" starts, then works his way through. First he gives a clear exposition of the general framework of Marxist theory: the law of value, the differences between value, use value and exchange value, the mode of production etc. All this is done quite well, though there are of course many many such general descriptions available in print. Harvey does seem to skip over the "transformation problem" somewhat, which may annoy those who consider it a major hurdle. Harvey, in my view with good reason, does not.
The next two chapters discuss production, distribution, surplus value and its realization and the relation to supply and demand. Particularly useful here are his explanations of the importance of the concept of value composition of capital, and the reduction of skilled to simple labour, where he addresses one of Von Böhm-Bawerk's better critiques of Marxism.
The next part of the book is perhaps the core of the book. Here, Harvey delves into the organization of capital, the various forms which it can take and how these interrelate, and the tendency of the rate of profit to fall. He shows how the various manifestations of capital can interfere with each other's functioning and how this creates the tendency towards crises. He then posits the problem of overaccumulation (rather than underdevelopment) as the first 'layer' or 'cut' of crisis theory.
After the reader has grasped all this, the second crucial part of the book follows in a rapid manner, introducing first the problematic of fixed capital and its relation to the law of value, and then the role of credit in capitalism. The first is not very satisfactorily resolved and is in my view probably the weakest part of his theory. Alan Freeman has since given a quite different solution to the same issue, but that does not seem to really solve the problem either. Perhaps this is one of the things Marxist political economy has yet to fully solve.
Harvey's demonstration of the role of credit is however masterful and extremely enlightening for the many who are confused by the vast array of forms in which credit appears in modern society. His emphasis on the importance of understanding the so-called "fictitious capital", that is advanced capital not yet backed by actual value through production, allows him to show the second major appearance of crises in capitalism as well as explaining the theory of rent in Marxism, which forms the subject of the chapter thereafter. He corrects Marx' somewhat excessively anti-distributive theory of rent and explains the role of agricultural technology. Harvey is in many parts of this chapter rather confusing in his terminology, but a careful reader can certainly grasp the issue.
At the end of the book Harvey can finally follow up on his own area of expertise. By explaining the role of spatial and temporal relations in the flow of capital and the necessity of 'exporting' the internal contradictions of capitalist social relations, he is able to form a theory of imperialism that is largely in accordance with that of Lenin, but without the theory of underdevelopment. It also puts a good perspective on Marx & Engels' many journalistic articles about India and colonialism. Finally he combines this with the earlier two aspects to form the third 'cut' of capitalist crisis theory, which takes every aspect of capitalism in its modern appearance into account.
On the whole, Harvey has done an unparallelled and magisterial work in creating an exposition of capitalism that is at once as in-depth as "Capital" and much clearer (and shorter!) than that, although of course without Marx no such thing could ever have been made.
There are a few things nevertheless not covered (fully) in the book. Harvey pays surprisingly little attention to urban geography and (sub)urbanization as a factor in capitalism. Furthermore his theory of the state is a hodgepodge of different roles, which he never unites into one whole. Finally, people experienced in handling Marxist theory might have problems with Harvey's generally structuralist approach, which leaves relatively very little room for the autonomous significance of class struggle. Harvey mostly relegates that to the fields of production processes and labour mobility. Because of this, Lebowitz' "Beyond Capital" should probably be read alongside it as a complementary contribution, analyzing the same from the side of wage-labour.