Surface magnetism of cool stars

Magnetic fields are essential ingredients of many physical processes in the interiors and envelopes of cool stars. Yet their direct detection and characterization is notoriously difficult, requiring high-quality observations and advanced analysis techniques. Significant progress has been recently achieved by several types of direct magnetic field studies on the surfaces of cool, active stars. In particular, complementary techniques of field topology mapping with polarization data and total magnetic flux measurements from intensity spectra have been systematically applied to different classes of active stars, leading to interesting and occasionally controversial results. In this paper, we summarize the current status of direct magnetic field studies of cool stars and investigations of surface inhomogeneities caused by the field, based on the material presented at the Cool Stars 19 splinter session.