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.
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