  The EUV (100-912 {\AA}) is a spectral region notoriously difficult to observe
due to attenuation by neutral hydrogen gas in the interstellar medium. Despite
this, hundreds to thousands of nearby stars of different spectral types and
magnetic activity levels are accessible in the EUV range. The EUV probes
interesting and complicated regions in the stellar atmosphere like the lower
corona and transition region that are inaccessible from other spectral regions.
In this white paper we describe how direct EUV observations, which require a
dedicated grazing-incidence observatory, cannot yet be accurately substituted
with models and theory. Exploring EUV emission from cool dwarf stars in the
time domain can make a major contribution to understanding stellar outer
atmospheres and magnetism, and offers the clearest path toward detecting
coronal mass ejections on stars other than the Sun.
