The book contains a broad overview and critical analysis of the philosophies of mathematics proposed in the West in the 20th century. Not only the most famous trends, such as platonism, formalism or constructivism, are considered, but also nominalism, logicism, realism, phenomenology, naturalism, semiotics, structuralism, deductivism, fallibilizi, empiricism, etc. In each of the considered movements, philosophical principles, methods and tools of importance to mathematics are discussed.