NGC 4945 is with D ~3-4 Mpc one of the nearest starburst galaxies known and a goldmine for molecular cloud research. A multi-line mm-wave study has been carried out towards its nuclear region with the Swedish-ESO Sub-millimetre Telescope (SEST). The study covers the frequency range from 82 GHz to 354 GHz and includes 80 transitions of 19 molecules, including rare isotope-bearing species. Applying a Large Velocity Gradient (LVG) code to the data, H2 densities and column densities of 22 molecular species are calculated. Many of these species indicate the presence of a prominent high density interstellar gas component characterized by n H2 ~105cm-3. Abundances of molecular species are calculated and compared with abundances observed toward the starburst galaxies NGC 253 and M 82 and galactic sources. Apparent is an ‘overabundance’ of HNC and CN in the nuclear environment of NGC 4945. NGC 4945 is the second known starburst galaxy with an HNC/HCN abundance ratio ≥1. Carbon, nitrogen, oxygen and sulfur isotope ratios are also determined. The data indicate that high 18O/17O, low 16O/18O and 14N/15N and perhaps also low 32S/34S ratios (6.4±0.3, 195±45, 105±25 and 13.5±2.5, respectively) are characteristic properties of a starburst environment in an advanced evolutionary stage.