  X-ray emission from stars in the cool half of the Hertzsprung-Russell diagram
is generally attributed to the presence of a magnetic corona that contains
plasma at temperatures exceeding 1 million K. Coronae are ubiquitous among
these stars, yet many fundamental mechanisms operating in their magnetic fields
still elude an interpretation through a detailed physical description. Stellar
X-ray astronomy is therefore contributing toward a deeper understanding of the
generation of magnetic fields in magnetohydrodynamic dynamos, the release of
energy in tenuous astrophysical plasmas through various plasma-physical
processes, and the interactions of high-energy radiation with the stellar
environment. Stellar X-ray emission also provides important diagnostics to
study the structure and evolution of stellar magnetic fields from the first
days of a protostellar life to the latest stages of stellar evolution among
giants and supergiants. The discipline of stellar coronal X-ray astronomy has
now reached a level of sophistication that makes tests of advanced theories in
stellar physics possible. This development is based on the rapidly advancing
instrumental possibilities that today allow us to obtain images with
sub-arcsecond resolution and spectra with resolving powers exceeding 1000.
High-resolution X-ray spectroscopy has, in fact, opened new windows into
astrophysical sources, and has played a fundamental role in coronal research.
  The present article reviews the development and current status of various
topics in the X-ray astronomy of stellar coronae, focusing on observational
results and on theoretical aspects relevant to our understanding of coronal
magnetic structure and evolution.
