  Cosmic Microwave Background (CMB) Anisotropies is a subject of intensive
research in several fields of sciences. In this paper we start a systematic
development of basic notions and theory in statistics according to the
application for CMB. The main result of this paper is the necessary and
sufficient condition for isotropy of a non-Gaussian field in terms of spectra.
Clear formulae for bi-, tri- and polyspectra and bi-, tri-, and higher order
covariances are also given. Keywords: Bispectrum, Trispectrum, Angular
poly-Spectra, Cosmic microwave background radiation; Gaussianity; spherical
random fields
