Skobeltsyn Institute of Nuclear Physics
Lomonosov Moscow State University

The present paper opens series of the works devoted to the detailed exposition
of the meson spectroscopy questions at the present stage. The theoretical and
experimental study of XX century last decade give an evidence of new particle
existence which are same "white"\ as the famous mesons, but have another
internal structure. They were called by Glueball (coupled gluon state) and
Hybrid (coupled quarks and gluons states). This is a quite new class of matter
which is called by QCD Exotics. Part I is devoted to the description of quantum
numbers of Exotic meson states.