  We study continuous Anderson Hamiltonians with non-degenerate single site
probability distribution of bounded support, without any regularity condition
on the single site probability distribution. We prove the existence of a strong
form of localization at the bottom of the spectrum, which includes Anderson
localization (pure point spectrum with exponentially decaying eigenfunctions)
with finite multiplicity of eigenvalues, dynamical localization (no spreading
of wave packets under the time evolution), decay of eigenfunctions
correlations, and decay of the Fermi projections. We also prove log-H\" older
continuity of the integrated density of states at the bottom of the spectrum.
