  In this article we review essential natures of superconductivity in strongly
correlated electron systems (SCES) from a universal point of view. After
summarizing experimental results on typical materials such as high-$T_{\rm c}$
cuprates, BEDT-TTF organic superconductors, and ruthenate Sr$_2$RuO$_4$, we
review theoretical results for the analyses of superconducting properties of
these materials based on the Fermi-liquid framework in the single- and
multi-band Hubbard model. It is emphasized that the Coulomb interaction induces
various types of anisotropic superconductivity, $d$- or p-wave, through the
momentum dependence of quasi-particle interaction. While some inter-orbital
interactions exist in the multi-orbital system, anisotropic superconductivity
is induced by essentially the same mechanism, namely the momentum dependence of
quasi-particle interaction. This is the understanding of the mechanism of
superconductivity in SCES. Another important purpose of this article is to
review anomalous electronic properties of SCES near the Mott transition.
Especially, we focus on pseudogap phenomena observed in under-doped cuprates
and organic superconductors. According to the recent theory, superconducting
fluctuations, inherent in the quasi-two-dimensional and strong-coupling
superconductors, are the origin of the pseudogap formation. Based on the
microscopic theory of the superconducting fluctuations, we discuss the magnetic
and transport properties as well as the single-particle spectra in the
pseudogap state. As for heavy-fermion superconductors, experimental results are
reviewed and several theoretical analyses on the mechanism are provided based
on the same viewpoint as explained above.
