In Das Capital or Capital: Critique of Political Economy Karl Marx promotes his system of economics and proposes its adoption after the rejection of the capitalist system. He devotes Volume I to analyzing and criticizing capitalism. His main objection to the dominant economic system is its propagation of the class struggle, pitting people against one another. This is the establishment of his argument for economic change. Regrettably this is the only volume which was published during Marx' lifetime. The majority of his fame and influence occurred after his death.
Volume II introduces the concepts of value and surplus. The money owner, merchant, and entrepreneur are the main players in the production of capital. The laborer, however, also functions as a producer, a producer of labor, which is the basis of Marx subsequent arguments. To Marx understanding this particular piece of economy is essential to understanding all of his other discourse. Basically he believes that capitalism leads to inevitably unbalanced supply and demand which in turn deepens class struggles as wealth and labor are unusually distributed throughout society. His argument is sound because those periods of disequilibrium do occur in the capitalist system, but Marx neglects to account for human nature the way that Adam Smith bases his arguments. They are arguing on two separate planes, but Marx' German rationalism serves him well in his use of logic to disprove the capitalist system.
Engels compiled Volume III from Marx' notes, so it's structure and tone are slightly different from the rest of the book. He addresses seven topics: converting surplus to profit, converting profit to average profit, profit's tendency to fall, converting commodity and money capital into commercial and merchant's capital, dividing profit for interest bearing capital, changing surplus into ground rent, and revenue. The basic argument here is that the rate of profit falls when organic fixed capital becomes more expensive as a result of technological advancements. By Marx' logic, the inevitable failure of the capitalist system will result in the formation of an equally organic, equally necessary, and entirely new economic system. His goal is to correctly interpret the social functions of economy in the past and present in order to predict the system which will best benefit the whole of society in the future. He's placed himself in the position of a sort of economic prophet, interpreting present signs for future prediction. While Marx never witnessed the acceptance of his ideas, he has profoundly influenced subsequent generations of economists.