High temperature superconductivity is an interesting and fascinating phenomenonrnin which certain materials conduct electricity with zero electrical resistance andrnexpulsion of interior magnetic field with superconducting transition temperaturernhigher than 30 K. This was unexpectedly discovered in copper oxide materialsrnby Bednorz andMuller. After this discovery, a search for new high temperaturernsuperconducting families began and still going on.rnIn this thesis, we study high temperature superconductivity involving cupraternand pnicides theoretically. In order to look for this, we consider a model Hamiltonianrnconsisting of kinetic energy term, magnetic energy term and electronspinrnfluctuation term. and we used Green function formalism to calculate superconductingrntransition temperature and obtain an expression for the superconductingrnorder parameter for high temperature superconductors analytically.rnWe get the superconducting transition temperatures for YBa2Cu3O6:93 andrnCaNdFeAsF, 92.4 K and 56 K respectively as they being high Tc materials in theirrnrespective series. The spin fluctuation/magnon/ as a possible mechanism forrnhigh temperature superconductivity is also highlighted, as yet there is no consensusrnfor the mechanism for high temperature superconductivity in these system