The basic concepts and the generation principle of PIM at microwave frequencies are discussed. The polynomial and matrix representations for arbitrary odd-order PIM amplitudes are derived. General mathematical formulas regarding the third order and fifth order PIM power levels. As an example, prediction of the fifth order PIM power level of metallic contact at microwave frequencies with third order measured values is carried out by computer program. Calculated values are compared with experimental results, indicating that predicted result practically agrees with the measured one.