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This paper presents the first results of the study of high-energy electron and muon neutrino charged-current interactions in the FASER emulsion/tungsten detector of the FASER experiment at the LHC. A subset of the FASER volume, which corresponds to a target mass of 128. 6~kg, was exposed to neutrinos from the LHC pp collisions with a centre-of-mass energy of 13. 6~TeV and an integrated luminosity of 9. 5 fb^-1. Applying stringent selections requiring electrons with reconstructed energy above 200~GeV, four electron neutrino interaction candidate events are observed with an expected background of 0. 025^+0. 015-₀. ₀₁₀, leading to a statistical significance of 5. 2. This is the first direct observation of electron neutrino interactions at a particle collider. Eight muon neutrino interaction candidate events are also detected, with an expected background of 0. 22^+0. 09-₀. ₀₇, leading to a statistical significance of 5. 7. The signal events include neutrinos with energies in the TeV range, the highest-energy electron and muon neutrinos ever detected from an artificial source. The energy-independent part of the interaction cross section per nucleon is measured over an energy range of 560--1740 GeV (520--1760 GeV) for ₑ (_) to be (1. 2-₀. ₇^+0. 8) 10^-38~cm^2\, GeV^-1 ( (0. 50. 2) 10^-38~cm^2\, GeV^-1), consistent with Standard Model predictions. These are the first measurements of neutrino interaction cross sections in those energy ranges.
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