Mass as a physical quantity and its measurement are described. After some historical remarks, a short summary of the concept of mass in classical and modern physics is given. Principles and methods of mass measurements, for example as energy measurement or as measurement of weight forces and forces caused by acceleration, are discussed. Precision mass measurement by comparing mass standards using balances is described in detail. Measurement of atomic masses related to 12 C is briefly reviewed as well as experiments and recent discussions for a future new definition of the kilogram, the SI unit of mass.