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The neutron total cross sections for hydrogen, deuterium, and tritium have been measured with the neutron-time-of-flight technique. The tritium data span the neutron energy range from 60 keV to 80 MeV, with an overall systematic uncertainty which varies from 0.5% for energies below 17 MeV to 2% at the highest energy measured; the statistical uncertainties exceed these values only below 200 keV and above 7 MeV. The three-mole high-pressure gas samples were nearly isotopically pure. Excellent agreement is found with accepted cross sections for hydrogen and deuterium, and with previous Van de Graaff measurements for tritium except at the lowest-energy point at 290 keV. A minimum in the cross section near 600 keV (with a rise at lower energy) is newly observed. The cross section in the heretofore unexplored energy region between 7 and 14 MeV exhibits no structure, and thus no evidence for the existence of a bound fourneutron state. The extrapolated zero-energy cross section is found to be 1.70\ifmmode\pm\else\textpm\fi{}0.03 b, in sharp disagreement with previous thermal-energy observations, but in agreement with calculations which also yield the currently accepted coherent scattering length 3.73 fm. Agreement with a prediction from an analysis of $p$-$^{3}\mathrm{He}$ data is within 1% at the resonance peak near 3.5 MeV, but the data differ from this prediction by as much as 6% at lower and higher energies. Thus, within the framework of a suitable theoretical analysis, the present data might provide a measure of the departure from charge symmetry of the nuclear force.NUCLEAR REACTIONS Measured $\ensuremath{\sigma}({E}_{n})$ for $^{1}\mathrm{H}$, $^{2}\mathrm{H}$, 0.06-80 MeV; LINAC, NTOF technique, isotopic, high-pressure gas samples; tritium; four-nucleon system; four-neutron state; scattering length; charge symmetry; $R$ matrix.