  We report muon spin rotation (${\mu}$SR) experiments together with
first-principles calculations on microscopic properties of superconductivity in
the kagome superconductor LaRu$_3$Si$_2$ with $T_{\rm c}$ ${\simeq}$ 7K. We
find that the calculated normal state band structure features a kagome flat
band and Dirac as well as van Hove points formed by the Ru-$dz^2$ orbitals near
the Fermi level. Below $T_{\rm c}$, ${\mu}$SR reveals isotropic type-II
superconductivity, which is robust against hydrostatic pressure up to 2 GPa.
Intriguingly, the ratio 2$\Delta/k_{\rm B}T_{\rm c}$ ${\simeq}$ 4.3 (where
${\Delta}$ is the superconducting energy gap) is in the strong coupling limit,
and $T_{\rm c}$/$\lambda_{eff}^{-2}$ (where ${\lambda}$ is the penetration
depth) is comparable to that of high-temperature unconventional
superconductors. We also find that electron-phonon coupling alone can only
reproduce small fraction of $T_{\rm c}$ from calculations, which suggests other
factors in enhancing $T_{\rm c}$ such as the correlation effect from the kagome
flat band, the van Hove point on the kagome lattice, and high density of states
from narrow kagome bands. Our experiments and calculations taken together point
to strong coupling and the unconventional nature of kagome superconductivity in
LaRu$_3$Si$_2$.
