We present a method which delivers a continuous, high-density beam of slow and internally cold polar molecules. In our source, warm molecules are first cooled by collisions with a cryogenic helium buffer gas. Cold molecules are then extracted by mean
s of an electrostatic quadrupole guide. For ND$_3$ the source produces fluxes up to $(7 pm ^{7}_{4}) times 10^{10}$ molecules/s with peak densities up to $(1.0 pm ^{1.0}_{0.6}) times 10^9$ molecules/cm$^3$. For H$_2$CO the population of rovibrational states is monitored by depletion spectroscopy, resulting in single-state populations up to $(82 pm 10)%$.
