A Goddard High Resolution Spectrograph archival study of the interstellar absorption lines in the line of sight to the H I-rich, starburst dwarf galaxy NGC 1705 in the 1170 to 1740 Angstrom range at similar to 120 km s(-1) resolution is presented. The absorption features arising because of photospheric lines are distinctly different from the interstellar lines: the photospheric lines are weak, broad (equivalent widths >1 Angstrom), asymmetric, and centered around the systemic LSR velocity of NGC 1705 (similar to 610 km s(-1)). The interstellar lines consist of three relatively narrow components at LSR velocities of -20, 260, and 540 km s(-1), and include absorption by neutral atoms (N I lambda 1200 triplet and O I lambda 1302), singly ionized atoms (Si II lambda lambda 1190, 1193, 1260, 1304, and 1526, S II lambda 1253, C II lambda 1334, C II* lambda 1336, Fe II lambda 1608, and Al II lambda 1670), and atoms in higher ionization states (Si III lambda 1206, Si Iv lambda lambda 1393, 1402, and C Iv lambda lambda 1548, 1550). The Si Iv and C Iv absorption features have both interstellar and photospheric contributions. In an earlier study, Sahu & Blades identified the absorption system at -20 km s(-1) with Milky Way disk/halo gas, and the 260 km s(-1) system with a small, isolated high-velocity cloud HVC 487, which is probably associated with Magellanic Stream gas. The 540 km s(-1) absorption system is associated with a kiloparsec-scale expanding, ionized supershell centered on the super-star cluster NGC 1705-1. The analysis presented in this paper consists of (1) a list of all interstellar absorption features with greater than 3 sigma significance and their measured equivalent widths, (2) plots of the lines in the various atomic species together with the results of nonlinear least-squares fit profiles to the observed data, and (3) unpublished 21 cm maps from the Wakker & van Woerden survey showing the large-scale H I distribution in the region near the NGC 1705 sight line and HVC 487. Furthermore, weak N I lambda 1200 triplet absorption for the supershell component is reported, which in the absence of dust depletion and ionization corrections implies a low N abundance. A low N abundance for the supershell is consistent with an interpretation of nucleosynthetic enrichment by time-delayed primary nitrogen production, the age estimate of (10-20) x 10(6) yr for the central super-star cluster NGC 1705-1 of Heckman & Leitherer, and the underabundance of Fe reported by Sahu & Blades. However, using the N I lambda 1200 triplet alone to estimate the total N abundance could result in a severe underestimation of this quantity: although N does not deplete onto interstellar dust grains, photoionization and collisional ionization effects could increase the fraction of N found in higher ionization stages. Uncertainties in the total N abundance caused by photoionization and collisional ionization effects can only be addressed by future observations of the higher ionization lines, namely, N II lambda 1084 and N III lambda 989.