Abstract
A review of spectroscopic methods for observations of stars in searching for and studying exoplanets is presented. Instrumental errors in measuring radial velocities and strategies to decrease (or fundamentally eliminate) them are considered. The role of astrometric and photometric methods is pointed out. The results of the study of the chemical composition of parent stars and the spectroscopy of transit phenomena are discussed. Some promising directions are evaluated. The development of Russian ground-based and orbital instruments for spectroscopy and spectropolarimetry of stars is reported.
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