Gauge-invariant magnetic monopole dominance in quark confinement

We show that a gauge-invariant magnetic monopole can be defined in Yang-Mills theory without matter fields, using a non-Abelian Stokes theorem and change of field variables a la Cho-Faddeev-Niemi, instead of using the Abelian projection. In fact, we give a first exact solution representing a magnetic monopole loop due to a meron pair with the non-trivial Pontryagin index. In addition, we summarize remarkable results of numerical simulations based on a new formulation of Yang-Mills theory: 'Abelian' dominance and magnetic monopole dominance in the string tension. Finally, we discuss a novel feature in the case of SU(3) gauge group.