Stellar astronomy is the study of stars and the phenomena exhibited by the various forms/developmental stages of stars.
Stellar astronomy has two main approaches, observational and theoretical.
Observational stellar astronomy comprises optical observations, such as photometry (i.e., the study of color and intensity variations in the electromagnetic radiation detected from stars) and spectroscopy (i.e., the study of the variation of intensity with electromagnetic wavelength for a given star -- its "spectrum"), and observations in all non-optical regions of the electromagnetic spectrum as well.
Even the detection of gravitons or neutrinos could fall under the rubric of "observational stellar astronomy," although those sorts of observations generally have more specialized subfields of their own.
Theoretical stellar astronomy includes various forms of stellar modeling as well as models of specific phenomena which have been observationally associated with stars (such as magnetic reconnection models for stellar flares or Raymond-Smith models for high-temperature plasmas which may surround stars or which may be found in other astronomical contexts).
It runs the gamut of physical disciplines as they have been applied to astronomy, although again some physical models are more applicable to stellar astronomy than others -- N-body simulations are more often found in dynamical astronomy as applied to multi-body systems or even to interacting galaxies, so the only place you're likely to find them in "stellar astronomy" is in relation to prestellar nebular dynamics (e.g., the work of Stu Weidenschilling and other presolar nebula theoreticians).