Proton total cross-sections on /sup 1/H, /sup 2/D, /sup 4/He, /sup 12 /C, and /sup 16/O have been measured in the energy range 180 to 560 Me V in a high precision transmission experiment with a statistical accuracy of +or-0.2%. Random errors are typically +or-0.5% for pp data, +or-1% for /sup 2/D and /sup 4/He, and +or-(1-3%) for /sup 12/C and /sup 16/O total cross-sections. Systematic errors of +or-(0.8-1%) in the /sup 1/H and /sup 2/D data originate mainly from uncertainties in applying the correct Coulomb-nuclear interference corrections to the measured partial cross-sections before extrapolating to the total cross-section at zero solid angle. The real parts of the nuclear spin- independent forward scattering amplitudes on /sup 4/He, /sup 12/C, and /sup 16/O were obtained in the same experiment by analysing the angular dependence of the partial cross-sections in the Coulomb- nuclear interference region. Total cross-sections are calculated in a Glauber-model approach, and the results are compared to this data