This book provides an introduction to Marxism as it emerged in the nineteenth century, examines what happened when it was put into practice in the twentieth century, and how we can make use of it now in anti-capitalist struggle. Marxism is described through a detailed account of three key component parts of Marxism, and how it engages with and transcends divisions between philosophy, sociology and economics. The book reviews the degeneration and distortion of Marxist politics under the baleful influence of Stalinism, and explores how we can put Marxist ideas to work, reviewing the contribution of revolutionary Marxists, Lenin and Trotsky, while acknowledging their faults and the role of anarchism as a radical resource. It shows how these ideas are relevant to contemporary culture, technology and politics, including the emergence of decolonial, ecological and feminist critique, redeeming the promise of Marxism to help us struggle for open communism.