Abstract: The results of calculation of fluxes of ultracold (UCNs), very cold, and cold neutrons at the output of neutron guides of the UCN source with superfluid helium at the WWR-M reactor are presented. UCN density ρ_35L = 1.3 × 10⁴ n/cm³ in the trap of the electric dipole moment (EDM) spectrometer was obtained by optimizing source parameters. This UCN density in the EDM spectrometer is two orders of magnitude higher than the UCN density at the output of the available UCN sources. The flux density of cold neutrons with a wavelength of 2–20 Å at the output of a neutron guide with a cross section of 30 × 200 mm² should be as high as 1.1 × 10⁸ n/(cm² s), while the flux density of very cold neutrons (50–100 Å) at the output of the same neutron guide should be 2.3 × 10⁵ n/(cm² s). An extensive program of fundamental and applied physical research was mapped out for this source.