  As astronomers increasingly exploit the information available in the time
domain, spectroscopic variability in particular opens broad new channels of
investigation. Here we describe the selection algorithms for all targets
intended for repeat spectroscopy in the Time Domain Spectroscopic Survey
(TDSS), part of the extended Baryon Oscillation Spectroscopic Survey within the
Sloan Digital Sky Survey-IV. Also discussed are the scientific rationale and
technical constraints leading to these target selections. The TDSS includes a
large "Repeat Quasar Spectroscopy" (RQS) program delivering ~13,000 repeat
spectra of confirmed SDSS quasars, and several smaller "Few-Epoch Spectroscopy"
(FES) programs targeting specific classes of quasars as well as stars. The RQS
program aims to provide a large and diverse quasar data set for studying
variations in quasar spectra on timescales of years, a comparison sample for
the FES quasar programs, and opportunity for discovering rare, serendipitous
events. The FES programs cover a wide variety of phenomena in both quasars and
stars. Quasar FES programs target broad absorption line quasars, high
signal-to-noise ratio normal broad line quasars, quasars with double-peaked or
very asymmetric broad emission line profiles, binary supermassive black hole
candidates, and the most photometrically variable quasars. Strongly variable
stars are also targeted for repeat spectroscopy, encompassing many types of
eclipsing binary systems, and classical pulsators like RR Lyrae. Other stellar
FES programs allow spectroscopic variability studies of active ultracool dwarf
stars, dwarf carbon stars, and white dwarf/M dwarf spectroscopic binaries. We
present example TDSS spectra and describe anticipated sample sizes and results.
