Molecular lines are used to trace the structure of the interstellar medium and the physical conditions of the gas in different environments, from high-z galaxies to protoplanetary disks. To fully benefit from the diagnostic power of molecular lines, the formation and destruction paths of the molecules, including the interplay between gas-phase and grain surface chemistry, must be quantitatively understood. Well-defined sets of observations of simple template sources are key to benchmark the predictions of theoretical models. With that motivation, this thesis is focused on the observation and analysis of an unbiased spectral line survey at 3, 2 and 1mm with the IRAM-30m telescope in the Horsehead nebula, with an unprecedented combination of bandwidth, high spectral resolution and sensitivity. Two positions were observed: the warm photodissociation region (PDR) and a cold condensation shielded from the UV field. Approximately 30 species, with up to 7 atoms plus their isotopologues, are detected. These data are complemented by high-angular resolution IRAM-PdB interferometric maps of specific species. The results of this thesis include the detection of CF+, a new diagnostic of the UV illuminated gas; the detection of a new species in the ISM, tentatively attributed to C3H+; a deep study of the abundance, spatial distribution and excitation conditions of H2CO, CH3OH and CH3CN, which reveals that photo-desorption of ices is an efficient mechanism to release molecules into the gas phase; and the first detection of the complex organic molecules, HCOOH, CH2CO, CH3CHO and CH3CCH in a PDR, which reveals the degree of chemical complexity reached in the UV illuminated neutral gas.
