The different ways for expressing the dependence of the scattering amplitude h(z) on its argument z are called representations of the scattering amplitude. In the component representation h(z) is expressed as a sum of more elementary functions. The component representation is proved to be unique. The determination of h(z) in regions with singularities is carried out for the cases which are inaccessible for Oehmes method. In suitable representations algebraic equations of the Low type are derived. These equations may have an advantage over the dispersion ones because the usual analytical properties of the scattering amplitude are necessary for their derivation. The possibilities for a natural classification of the scattering amplitudes are discussed.