We study the essential works of Karl Marx and Friedrich Engels, as well as their philosophical precursors and some influential variations of Marxism in the 20th and 21st century. We will discuss historical materialism, dialectical method, the Marxist theory of human nature and of alienation, ideology, class struggle, the relationship between substructure and superstructure, the labor theory of value, and Marx’s vision of communism. Perhaps most important, we will try to apply Marxist theory in its many variations to the pressing issues of our time, including racial and gender oppression, the ecological crisis, terrorism, war, imperialism, globalization, and what it means to be an anti-capitalist and the possibility of a socialist alternative in the twenty first century.