Unconventional superconductivity with either multi-component or multi-band, or with chirality

In this review article, we discuss unconventional superconductivity where the unconventionality comes either from the multi-component order parameter, or from the multi-band order parameter, or from the chirality of the pairing function. These three typical form of unconventional superconductivity are analyzed in connection with materials such as UPt3 and UGe2 as the first example. MgB2 is mentioned as the second case where two distinctive energy gaps exist on different Fermi surface sheets. Sr2RuO4 is taken up as an example for chiral superconductivity. Here the vortex state in the mixed state in each superconductor is focused on from the view point of their unconventionality.