The recent discovery of highÂ·Â·temperature superconductivity broughtrnabout the necessity of clal'ifying a set of questions. One of these is regardingrnthe electron pairing mechanism. Upto now, we have a well-developedrnmicroscopic theory of the conventional supel'conductivity, the so-called BCSrntheory. lIs we know, the pairing of electrons in this theory is realiz!!drnthrough the exchange of virtual phonons. This mechanism leads to the existencernof energy gap in the spectrum of elementary excitations of low-temperaturernsuperconductivity. And, in the absence of magnetic field, it is knownrnthat the normal-superconducting transition is second-order phase transition.rnThllS, the BCS theory gives the recipe for calculating all physical quantitiesrnof cOllventional superconductors.rnThe situation with the high-temperature superconductivity ;s much morerncomplex. The mechaIYism of high - Tc superconductivity is still unkonwn. Thisrnis the reason we decided to give in this pape!' the revie~1 of conventionalrnphenomenological t,heories of superconductivity and give new formulation ofrnBCS theory ;,/hich is b,lsed on retarded thermal Green's function method. Werna 1 so attempted to analyze the ava i1 ab 1 e eXperimenta 1 data on hi gh - T c andrnsome of the pairing mechanisms discussed in the literature. We finallyrnPt'oposed a mode 1 ~/hich can execute hi gil-temperature superconduct; vity wherern.' '?rnelectrons are paired by the exchange of virtual plasmons which can be OOset'vedrnin some specially prepal'ed thin films