Top quark production in the forward region in proton-proton collisions is observed for the first time. The W+b final state with W→μν is reconstructed using muons with a transverse momentum, pT, larger than 25 GeV in the pseudorapidity range 2.0<η<4.5. The b jets are required to have 5020  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 σ(top)[7  TeV]=239±53(stat)±33(syst)±24(theory)  fb,σ(top)[8  TeV]=289±43(stat)±40(syst)±29(theory)  fb.These results, along with the observed differential yields and c