The Ramsauer technique has been used to measure the absolute total electron-helium-atom scattering cross section as a function of electron energy from 0.30 to 28 eV with an estimated probable error of +/-3%. No "fine structure" has been observed at the lower electron energies studied. The variation of the cross section with energy for energies less than 3 eV is in reasonable agreement with the modified effective-range formula given by O'Malley, using a scattering length of 1.15a0. The cross section first increases with decreasing electron energy from 2.2Å2 at 28.0 eV to a maximum of 5.6Å2 at about 1.2 eV and then decreases to 5.4Å2 at 0.300 eV. The cross section has been found to decrease sharply with increasing energy at about 0.5 eV below the first excitation energy. This resonance, predicted by Baranger and Gerjuoy and originally observed by Schulz, first decreases with increasing energy to a minimum of about 10% below the background at 19.285+/-0.025 eV and then increases to a gentle maximum of about 3% above the background at 19.65+/-0.05 eV. The resolution of this resonance as well as the 10% decrease in the cross section at the minimum is determined by the half-width of the electron beam at this energy which is about 0.1 eV.