  The spectrum of an exoplanet reveals the physical, chemical, and biological
processes that have shaped its history and govern its future. However,
observations of exoplanet spectra are complicated by the overwhelming glare of
their host stars. This review chapter focuses on high resolution spectroscopy
(HRS; R=25,000-100,000), which helps to disentangle and isolate the exoplanet's
spectrum. At high spectral resolution, molecular features are resolved into a
dense forest of individual lines in a pattern that is unique for a given
molecule. For close-in planets, the spectral lines undergo large Doppler shifts
during the planet's orbit, while the host star and Earth's spectral features
remain essentially stationary, enabling a velocity separation of the planet.
For slower-moving, wide-orbit planets, HRS aided by high contrast imaging
instead isolates their spectra using their spatial separation. The lines in the
exoplanet spectrum are detected by comparing them with high resolution spectra
from atmospheric modelling codes; essentially a form of fingerprinting for
exoplanet atmospheres. This measures the planet's orbital velocity, and helps
define its true mass and orbital inclination. Consequently, HRS can detect both
transiting and non-transiting planets. It also simultaneously characterizes the
planet's atmosphere due to its sensitivity to the depth, shape, and position of
the planet's spectral lines. These are altered by the planet's atmospheric
composition, structure, clouds, and dynamics, including day-to-night winds and
its rotation period. This chapter describes the HRS technique in detail,
highlighting its successes in exoplanet detection and characterization, and
concludes with the future prospects of using HRS to identify biomarkers on
nearby rocky worlds, and map features in the atmospheres of giant exoplanets.
