Magnetic fields have been detected on stars across the H-R diagram and
substellar objects either directly by their effect on the formation of spectral
lines, or through the activity phenomena they power which can be observed
across a large part of the electromagnetic spectrum. Stars show a very wide
variety of magnetic properties in terms of strength, geometry or variability.
Cool stars generate their magnetic fields by dynamo effect, and their
properties appear to correlate - to some extent - with stellar parameters such
as mass, rotation and age. With the improvements of instrumentation and data
analysis techniques, magnetic fields can now be detected and studied down to
the domain of very-low-mass stars and brown dwarfs, triggering new theoretical
works aimed, in particular, at modelling dynamo action in these objects. After
a brief discussion on the importance of magnetic field in stellar physics, the
basics of dynamo theory and magnetic field measurements are presented. The main
results stemming from observational and theoretical studies of magnetism are
then detailed in two parts: the fully-convective transition, and the very-low
mass stars and brown dwarfs domain.Comment: 30 pages, 9 figures. Notes for lectures presented at the Evry
Schatzman school on "Low-mass stars and the transition from stars to brown
dwarfs", September 2011, Roscoff, France. To appear in the EAS Conference
Series, edited by C. Charbonnel, C. Reyle, M. Schulthei