  AMoRE searches for the signature of neutrinoless double beta decay of
$^{100}$Mo with a 100 kg sample of enriched $^{100}$Mo. Scintillating molybdate
crystals coupled with a metallic magnetic calorimeter operate at milli-Kelvin
temperatures to measure the energy of electrons emitted in the decay. As a
demonstration of the full-scale AMoRE, we conducted AMoRE-I, a pre-experiment
with 18 molybdate crystals, at the Yangyang Underground Laboratory for over two
years. The exposure was 8.02 kg$\cdot$year (or 3.89
kg$_{\mathrm{^{100}Mo}}\cdot$year) and the total background rate near the
Q-value was 0.025 $\pm$ 0.002 counts/keV/kg/year. We observed no indication of
$0\nu\beta\beta$ decay and report a new lower limit of the half-life of
$^{100}$Mo $0\nu\beta\beta$ decay as $
T^{0\nu}_{1/2}>3.0\times10^{24}~\mathrm{years}$ at 90\% confidence level. The
effective Majorana mass limit range is $m_{\beta\beta}<$(210--610) meV using
nuclear matrix elements estimated in the framework of different models,
including the recent shell model calculations.
