The axion is a hypothetical particle associated with spontaneously broken global Peccei-Quinn (PQ) symmetry introduced as a solution to the strong CP problem of quantum chromodynamics, and it is regarded as one of the best motivated candidates to be the dark matter of the universe. In comparison with other dark matter candidates, the axion possesses peculiar properties that they are produced non-thermally and expected to have an extremely small mass. In order to obtain a definite prediction for the mass, it is necessary to evaluate its relic abundance precisely by taking account of its production and evolution in the early universe. In this talk, we discuss the production mechanisms of axion dark matter in the early universe, particularly focusing on the production from cosmic strings and domain walls, which takes place if the PQ symmetry is broken after inflation. The prediction for the mass of axion dark matter is closely related with the early history of the universe, and such mass ranges are relevant to future experimental studies.
