  Muon spin relaxation ($\mu$SR) measurements on the new layered cobalt oxide
superconductor Na$_{0.35}$CoO$_{2}\cdot$1.3H$_{2}$O and its parent,
non-superconducting compounds, have revealed unconventional nature of
superconductivity through: (1) a small superfluid energy which implies a
surprisingly high effective mass of the charge carriers, approximately 100
times the bare electron mass; (2) the superconducting transition temperature
$T_{c}$ scaling with the superfluid energy following the correlations found in
high-$T_{c}$ cuprate and some other two-dimensional superconductors; (3) an
anisotropic pairing without broken time-reversal symmetry; and (4) the
proximity of a magnetically ordered insulating phase at Na$_{0.5}$CoO$_{2}$
below $T_{N}$ = 53 K.
