  Top quark production in the forward region in proton-proton collisions is
observed for the first time. The $W\!+\!b$ final state with $W\to\mu\nu$ is
reconstructed using muons with a transverse momentum, $p_{\rm T}$, larger than
25 GeV in the pseudorapidity range $2.0<\eta<4.5$. The $b$ jets are required to
have $50 < p_{\rm T} < 100$ GeV and $2.2 < \eta < 4.2$, while the transverse
component of the sum of the muon and $b$-jet momenta must satisfy $p_{\rm T} >
20$ GeV. The results are based on data corresponding to integrated luminosities
of 1.0 and $2.0$ fb$^{-1}$ collected at center-of-mass energies of 7 and 8 TeV
by LHCb. The inclusive top quark production cross-sections in the fiducial
region are $\sigma({\rm top})[7\rm{TeV}] = 239\pm53({\rm stat})\pm33({\rm
syst})\pm24({\rm theory})\,{\rm fb}$ and $\sigma({\rm top})[8\rm{TeV}] =
289\pm43({\rm stat})\pm40({\rm syst})\pm29({\rm theory})\,{\rm fb}$. These
results, along with the observed differential yields and charge asymmetries,
are in agreement with next-to-leading order Standard Model predictions.
