Relationships between Quark Masses and the CKM Elements

There are mysteries that the origin of small values in the Cabibbo-KobayashiMaskawa (CKM) matrix and the reason why the CKM matrix is close the unit matrix. We use the general quark mass matrices in order to solve the these problems. Up part and down part quark mass matrices are written in terms of six dimensionless parameters and six quark masses in the same form simultaneously. It is shown that two of the former six dimensionless parameters can be chosen to be any value. We obtain the exact relations between quark masses and the CKM elements. These results are obtained without any approximation and assumption. And next, an interesting parameter space is found, in which some instructive analytical relations between quark mass ratios and the CKM matrix elements can be derived. In particular, we reproduce the relations between masses and the CKM matrix elements without ne-tuning. In addition, some reviews and the related topics are included in this thesis.