I'm fairly well versed on all three volumes of Capital so I thought I might keep a thread up where I answer any questions for first time readers or those who aren't feeling equipped to dive in yet. I have a somewhat heterodox reading of Marx's project but it's well founded in Marx's own work and secondary literature. Marx was such a theoretically productive bastard that he often failed to understand just how wide the implications of his theoretical work stretched. I take Marx more as a critical social theorist than economist, but accept that Marx was always working on the terrain of classical political economy. Though it's important to remember that classical political economy is qualitatively different from modern economics and had wider social concerns.
Anyways, here's a rough sketch of Marx's project in Capital:
Volumes 1 and 2 deal with the essential, internal logic of capital when analyzed into its two distinctive spheres: production and circulation. The analytic separation is not a clean one though and often, elements of production and elements of circulation will find themselves theoretically enmeshed with one another in Volumes 1 and 2. This is to be expected given that the object of analysis is itself the unity of both of these moments in the total reproduction of the social whole.
The fundamental architectonic of the Critique of Political Economy can be roughly sketched as follows:
Volume 1: The Production of Capital
Production should here be understood as both production in its immediate presentation, as capital is commonly understood (industrial production of goods) and production in the mediated, theoretically constructed sense. Capital as a social relation is something that is produced in the immediate production process but not reducible to it. Others have suggested that Marx may have had in mind a meaning closer to "The Constitution of Capital".
Volume 1 has as its first goal, analyzing the immediately visible logic of capital: exchange. Through an analysis of the exchange relation, Marx lays down the logic of the commodity-form, the contradictory dynamics of the value-form, and the necessity of value's appearance in the money-form.
Capital proper only appears once these terms have been placed in their necessary relation to one another. The question becomes, where does the growth particular to capital come from given that the objects of exchange are all transformations of equivalent values? The answer is that there is a special commodity, labor-power.
The bulk of Volume 1 details the manner in which labour-power is incorporated into the production of commodities as the condition for the production of surplus value.
Marx ends by outlining some possible tendencies of long-term capitalist development and tracing the historical genesis of a social logic that presents itself as an ahistorical, structural whole.