Within the next few years, several instruments aiming at imaging extrasolar planets willsee first light. In parallel, low mass planets are being searched around red dwarfs whichoffer more favorable conditions – both for radial velocity detection and transit studies –than solar-type stars. We review recent advancements in modeling the stellar to substellartransition. The revised solar oxygen abundances and cloud models allow to reproduce thephotometric and spectroscopic properties of this transition to a degree never achievedbefore, but problems remain at the stellar-brown dwarf transition typical of theTeff range of characterizable exoplanets.

I review efforts to determine the form and any lower limit to the initial mass functionin the Galactic disk, using observations of low-mass stars and brown dwarfs in the field,young clusters and star forming regions. I focus on the methodologies that have been usedand the uncertainties that exist due to observational limitations and to systematicuncertainties in calibrations and theoretical models. I conclude that whilst it ispossible that the low-mass IMFs deduced from the field and most young clusters aresimilar, there are too many problems to be sure; there are examples of low-mass clusterIMFs that appear to be very discrepant and the IMFs for brown dwarfs in the field andyoung clusters have yet to be reconciled convincingly.

These lectures attempt to expose the most important ideas, which have been proposed toexplain the formation of stars with particular emphasis on the formation of brown dwarfsand low-mass stars. We first describe the important physical processes which trigger thecollapse of a self-gravitating piece of fluid and regulate the star formation rate inmolecular clouds. Then we review the various theories which have been proposed along theyears to explain the origin of the stellar initial mass function paying particularattention to four models, namely the competitive accretion and the theories basedrespectively on stopped accretion, MHD shocks and turbulent dispersion. As it is yetunsettled whether the brown dwarfs form as low-mass stars, we present the theory of browndwarfs based on disk fragmentation stressing all the uncertainties due to the radiativefeedback and magnetic field. Finally, we describe the results of large scale simulationsperformed to explain the collapse and fragmentation of molecular clouds.

Within less than two decades, the study of low-mass stars and brown dwarfs has bloomedinto one of the most active fields in astronomy. The M, L, T and Y dwarfs sequencesincludes objects spawning more than an order of magnitude in absolute temperature, from4000 K down to room temperature, and nearly fills the entire temperature gap between thecoolest stars and our Solar System’s giant planets. I present an overview of thelarge-scale surveys that led to the discovery of a population of ultracool dwarfs in ourimmediate galactic vicinity, their classification and various noteworthy spectroscopicfeatures found only in these objects. I provide an outline of photometric variabilitystudy of L and T dwarfs, which opens a unique window on the atmospheric phenomenon at playin their atmospheres. Finally, I summarize the capabilities of an upcoming instrument, theSPIRou near-infrared, high-resolution spectropolarimeter, that will be available to theCFHT communities in 2015. SPIRou will be a unique tool for the study of cool dwarfs, andwill be used to undertake an ambitious survey of habitable Earth-sized planets aroundnearby M dwarfs.

Magnetic fields have been detected on stars across the H-R diagram and substellar objectseither directly by their effect on the formation of spectral lines, or through theactivity phenomena they power which can be observed across a large part of theelectromagnetic spectrum. Stars show a very wide variety of magnetic properties in termsof strength, geometry or variability. Cool stars generate their magnetic fields by dynamoeffect, and their properties appear to correlate – to some extent – with stellarparameters such as mass, rotation, and age. With the improvements of instrumentation anddata analysis techniques, magnetic fields can now be detected and studied down to thedomain of very-low-mass stars and brown dwarfs, triggering new theoretical works aimed, inparticular, at modelling dynamo action in these objects. After a brief discussion on theimportance of magnetic field in stellar physics, the basics of dynamo theory and magneticfield measurements are presented. The main results stemming from observational andtheoretical studies of magnetism are then detailed in two parts: the fully-convectivetransition, and the very-low mass stars and brown dwarfs domain.

The metallicity measures the fraction of the star that is made of elements heavier thanhelium. It is intimately related to the stellar structure and composition and thus playsan important role in a broad range of astrophysical cases, from stellar populations toplanet formation. This chapter aims to review the recent observational efforts to measurethe metallicity of M dwarfs and to screen few astrophysical cases which have benefitedfrom quantitative metallicity analysis.