Intellectual development of Marx
Marx's intellectual development starts with his Hegelian-inspired views, which he lays out in The Paris Manuscripts, where he was concerned with the idea of alienation. After leaving it unfinished, he moves on to The German Ideology, where he focuses on historical materialism heavily influenced by Adam Smith's notion of division of labor as a reason for the evolution of societies. In Grundrisse, Marx brings back the idea of alienation and replaces the division of labor with private property as the primary variable of his social analysis. Moreover, in Grundrisse, Marx also moves away from a uni-linear and deterministic view of history in favor of a multi-linear and more open one.
Das Kapital
In contrast to all other works, Das Kapital is one of Marx's only works that he saw as ready to be published (volume I because the other two volumes of Marx were published by Engels' after his death).
Labor power as a commodity
The labor theory of value starts with Locke's observation that labor is responsible for nine-tenths of the value created. Adam Smith takes the concept, and while he agrees with the idea that labor creates most of the value, he disagrees with its distribution because, in civil society, there exists accumulation of capital which creates another two important variables in the process of distributing that value, namely profit and rent. Overall, Adam Smith sees value as distributed in a fair way between three distinct factors: labor, capital, and land.
Acronyms: C, V, and S
In Marx's notation, C refers to constant capital, the investment required to utilize labor properly. At the same time, V is the variable capital or the wages of the workers. S stands for the surplus that the capitalist generates from selling his goods after subtracting the other costs associated with production (from investment to wages and rent).
Radicalizing Adam Smith
Marx radicalizes Adam Smith's work and states that all constant capital was once labor and was converted into its current form (capital) during the process of accumulation. Moreover, Marx also acknowledges that given that the surplus is a by-product of the labor process, it thus belongs solely to the workers (in contrast with the capitalists pocketing that difference).
Theory of exploitation
One of the lasting contributions of Marx to the field of social sciences is his theory of exploitation.
The essence of exploitation is the idea that the capital provided in the current production cycle is labor appropriated by the capitalist from an earlier cycle (through the surplus value).
Types of production
Marx takes Adam Smith's notion of commercial society and expands it by breaking it apart into two types of production: the commodity mode production and the capitalist mode of production.
The "petty" commodity mode of production is one where the cycle involves buying one commodity for another without a straightforward process of transformation in between each cycle.
"So you needed eggs. You brought shoes on the market, you sold shoes on the market [...] for money, then you went to the farmer and you bought the eggs so you could have scrambled eggs."
Commercial societies are mainly focused on satisfying basic needs (subsistence), and thus the alienation in this mode of production tends to be minimal. On the other hand, the capitalist mode of production goes beyond subsistence and focuses solely on profit-making as its primary goal.