This thesis presents the development of kinetic inductance detectors targeted for applications in far-infrared spectroscopy in astrophysics. The formation and evolution of galaxies across cosmic time is one of the key areas of exploration in modern astrophysics. The star formation rate density peaks at a redshift of around z=2, when the universe was dominated by dusty star-forming galaxies whose optical and ultraviolet radiation are significantly obscured and thermally reprocessed by dust into infrared radiation. A swath of fine-structure lines in the far-infrared serve as tracers of star formation activity in these galaxies, and far-infrared continuum and line emission are unobscured by dust. However, detecting these lines in individual galaxies is difficult and time consuming with currently-available infrared instruments. The Terahertz Intensity Mapper (TIM) experiment is a balloon-borne telescope spectrometer that will observe these galaxies leading back to the era of peak star formation. TIM will use the intensity mapping technique to create a three-dimensional map, incorporating the spectral dimension as the line-of-sight coordinate. This measurement will survey the aggregate star-formation activity as a function of redshift of the total galaxy population without a flux limit. TIM will incorporate two grating spectrometer modules to observe the 240-420 micron wavelength band with spectral resolution R = 250, each with 1800 low-noise kinetic inductance detectors (KIDs) in its focal plane. I present the development and testing of prototype KID arrays targeted for use on TIM. KIDs are superconducting microresonators that serve as radiation detectors. They rely on the kinetic inductance effect, which causes a shift in resonant behavior when incident photons are absorbed by Cooper pairs in the superconductor material. I present characterization results from two 45-pixel KID arrays fabricated out of thin-film aluminum on silicon substrates. I demonstrate that their device performance meets the sensitivity and noise requirements for the TIM experiment.