Schumpeter's vast erudition is apparent in his posthumous History of Economic Analysis, although some of his judgments seem quite idiosyncratic. For instance, Schumpeter thought that the greatest 18th century economist was Turgot, not Adam Smith. Some of these judgments are partly explained by his opinion that there is one general system of economic analysis, and Leon Walras found it. Other economists are rated by how much of Walras' theory could be read into them. Schumpeter criticized John Maynard Keynes and David Ricardo for the "Ricardian vice". According to Schumpeter, Ricardo and Keynes reasoned in terms of abstract models, where they would freeze all variables but a couple. Then they could argue that one caused the other in a simple monotonic fashion. Voila, one could easily deduce policy conclusions directly from a highly abstract theoretical model.
Schumpeter's relationships with the ideas of other economists were quite complex in his most important contributions to economic analysis - the theory of business cycles and development. From the above, the reader might conclude that Schumpeter followed Walras and that his analysis shared nothing in common with Keynes. But this conclusion would be wrong, as illustrated by Schumpeter's The Theory of Economic Development. Schumpeter starts with a stationary state, which he thinks is described by Walrasian equilibrium. Schumpeter describes the stationary state as a "circular flow." The hero of his story, though, is, in fine Austrian fashion, the entrepreneur. The entrepreneur disturbs this equilibrium and is the cause of economic development, which proceeds in cyclic fashion along several time scales. In fashioning this theory connecting innovations, cycles, and development, Schumpeter kept alive the Russian communist Kondratiev's ideas on 50-year cycles, Kondratieff Waves.
So in Schumpeter's theory Walrasian equilibrium is not adequate to capture the key mechanisms of economic development. Schumpeter also thought that the institution enabling the entrepreneur to purchase the resources needed to realize his or her vision was a well-developed capitalist financial system, including a whole range of institutions for granting credit. One could divide economists among (1) those who emphasized "real" analysis and regarded money as merely a "veil" and (2) those who thought monetary institutions are important and money could be a separate driving force. Both Schumpeter and Keynes were among the latter. Nevertheless, Schumpeter, who was a conservative, rejected Keynesianism. Some have seen this to be partly due to jealousy - Schumpeter might have seen that he would be judged by history as the second-greatest economist of his day, and he knew who would be first.
Schumpeter's most popular book in English is probably ''Capitalism, Socialism, and Democracy''. This book opens with a good treatment of Marx. Schumpeter is quite sympathetic to Marx's analysis, although Schumpeter concludes capitalism will be replaced by socialism for non-Marxist reasons. It is in this book that Schumpeter's characterizes capitalism by the phrase "creative destruction" in which old ways of doing things are endogenously destroyed and replaced by the new. Schumpeter thinks that the success of capitalism will lead to a form of corporations and a fostering of values, especially among intellectuals, of hostility to capitalism. The intellectual and social climate needed to allow entrepreneurship to thrive will not exist in advanced capitalism and it will be succeeded by socialism of some form or another. There will not be a revolution, but merely a trend in parliaments to elect social democratic parties of one stripe or another. Schumpeter emphasizes that he is analyzing trends, not engaging in political advocacy here. Some have thought John Kenneth Galbraith was influenced in his The New Industrial State by Schumpeter's views on corporations.
Schumpeter's views are most influential today among heterodox economists, especially European, who are interested in industrial organization, evolutionary theory, economic development, and chaotic dynamics. These economists tend to be on the other end of the political spectrum as Schumpeter and are equally influenced by Keynes, Karl Marx, and Thorstein Veblen.