  We have measured upper-critical-field $H_{\text c2}$, specific heat C, and
tunneling spectra of the intermetallic perovskite superconductor MgCNi${}_3$
with a superconducting transition temperature $T_{\text c}\approx 7.6$ K. Based
on these measurements and relevant theoretical relations, we have evaluated
various superconducting parameters for this material, including the
thermodynamic critical field $H_{\text c}$(0), coherence length $\xi$(0),
penetration depth $\lambda$(0), lower-critical-field $H_{\text c1}$(0), and
Ginsberg-Landau parameter $\kappa$(0). From the specific heat, we obtain the
Debye temperature $\it \Theta_{\text D} \approx$ 280 K. We find a jump of
$\Delta C/\gamma T_{\text c}$=2.3 at $T_{\text c}$ (where $\it \gamma$ is the
normal state electronic specific coefficient), which is much larger than the
weak coupling BCS value of 1.43. Our tunneling measurements revealed a gap
feature in the tunneling spectra at $\it \Delta$ with $2\it {\Delta}/{\text
k}_{\text B}T_{\text c}\approx$ 4.6, again larger than the weak-coupling value
of 3.53. Both findings indicate that MgCNi$_3$ is a strong-coupling
superconductor. In addition, we observed a pronounced zero-bias conductance
peak (ZBCP) in the tunneling spectra.
  We discuss the possible physical origins of the observed ZBCP, especially in
the context of the pairing symmetry of the material.
