"Marxism" is a shitty ass synonym for Communism or Socialism. Marxism is a mode of thought, a methodology. Marx thought that everything in a society was based on its economy. Every element of a society could be traced to a fact of its economy which influenced everything else. So to study society is really to study economics.
Marx never actually advocated Communism. Marx thought it was a natural progression that the economies of the world would all pass through. According to Marx's timeline, all economies would become more capitalistic, and then the revolution would happen. He never advocated changing anything, he was just laying out what he thought would happen.