A multi-line millimeter-wave study of the nearby starburst galaxy NGC 4945 has been carried out using the Swedish-ESO Submillimeter Telescope (SEST). The study covers the frequency range from 82 GHz to 354 GHz and includes 80 transitions of 19 molecules. 1.3 mm continuum data of the nuclear source are also presented. A large number of molecular species indicate the presence of a prominent high density interstellar gas component characterized by n H 2 ∼10 5 cm −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 in the nuclear environment of NGC 4945. While the HNC/HCN J =1--0 line intensity ratio is ∼ 0.5, the HNC/HCN abundance ratio is ∼ 1. While HCN is subthermally excited (T ex ∼ 8 K), CN is even less excited (T ex ∼ 3--4 K), indicating that it arises from a less dense gas component and that its N =2--1 line can be optically thin even though its N =1--0 emission is moderately optically thick. Overall, fractional abundances of NGC 4945 suggest that the starburst has reached a stage of evolution that is intermediate between those observed in NGC 253 and M 82. Carbon, nitrogen, oxygen and sulfur isotope ratios are also determined. Within the limits of uncertainty, carbon and oxygen isotope ratios appear to be the same in the nuclear regions of NGC 4945 and NGC 253. High 18 O/ 17 O, low 16 O/ 18 O and 14 N/ 15 N and perhaps also low 32 S/ 34 S ratios appear to be characteristic properties of a starburst environment in which massive stars have had sufficient time to affect the isotopic composition of the surrounding interstellar medium.