  We give a theoretical framework for defining and extracting non-Abelian
magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study
quark confinement. Then we give numerical evidences that the non-Abelian
magnetic monopole defined in this way gives a dominant contribution to
confinement of fundamental quarks in SU(3) Yang-Mills theory, which is in sharp
contrast to the SU(2) case in which Abelian magnetic monopoles play the
dominant role for quark confinement.
