Michele Friend provides an introduction to the standard theories of mathematics - platonism and realism, logicism, formalism, constructivism, and structuralism - as well as to some of the less standard theories, such as psychologism, fictionalism, and Meinongian philosophy of mathematics. The author explains what characterises each theory, the differences between them, and some of the arguments in favour of and against the different positions. Introducing Philosophy of Mathematics also explores questions that occupy present-day philosophers and mathematicians, such as the relationship between good reasoning and mathematics, the problem of infinity, and whether we are more certain of mathematics than we are of everyday sense experience or science. Friend strikes a nice balance between conceptual accessibility and clear representation of the issues to enable readers to challenge existing positions.