Quantum Chromodynamics (QCD) is considered as a very strong candidate as a theory describing the strong interaction. However, it has to give answers about the phenomena believed to occur in nuclear matter such as the status of the bound states of the quarks in the nucleus and the absence of free quarks from the final states of the reactions. The possible deconfinement of the quarks(quark or quark-gluon plasma) at high temperature or density or both, is also a very important question which QCD. faces and which involves the study of thermodynamic aspects of QCD. The production of very hot and dense matter(quark-gluon plasma) in the laboratory may help us understand the phenomena occuring in the Supernovae, neutron stars and the early universe. The planned attempts to produce such an environment on a mini-scale at CERN in the near future has made this study even more important. Theoretical physicists are using different models and methods to predict the events in the quark-giuon plasma. One of the most promising method being used is Lattice gauge theory. The finite temperature lattice QCD. gives a strong signal of the phase transition from ordinary hadron matter to quark-gluon plasma at a critical temperature Tc=180 Mev which is unexpectedly very high and finite density lattice QCD. (quark number >0) can be considered as a possibility for correcting this . This method requires the determination of eigenvalues of a big sparse non-hermitian matrix and its inversion
