Karl Marx was a German philosopher, economist, and political theorist in the 19th century. He developed the socialist political model known as communism. Marx did not play a direct role in literary theory, but Eagleton relies on his insights throughout the book. Eagleton is a socialist, as he mentions in the book's conclusion, and he employs Marx's analysis of relationship between social classes to understand the relationship between the political ruling class and the ideology it perpetuates through literature.
Literary Theory: An Introduction