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

I review efforts to determine the form and any lower limit to the initial mass function in 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 used and the uncertainties that exist due to observational limitations and to systematic uncertainties in calibrations and theoretical models. I conclude that whilst it is possible that the low-mass IMFs deduced from the field and most young clusters are similar, there are too many problems to be sure; there are examples of low-mass cluster IMFs that appear to be very discrepant and the IMFs for brown dwarfs in the field and young clusters have yet to be reconciled convincingly.

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

Within less than two decades, the study of low-mass stars and brown dwarfs has bloomed into one of the most active fields in astronomy. The M, L, T and Y dwarfs sequences includes objects spawning more than an order of magnitude in absolute temperature, from 4000 K down to room temperature, and nearly fills the entire temperature gap between the coolest stars and our Solar System’s giant planets. I present an overview of the large-scale surveys that led to the discovery of a population of ultracool dwarfs in our immediate galactic vicinity, their classification and various noteworthy spectroscopic features found only in these objects. I provide an outline of photometric variability study of L and T dwarfs, which opens a unique window on the atmospheric phenomenon at play in their atmospheres. Finally, I summarize the capabilities of an upcoming instrument, the SPIRou near-infrared, high-resolution spectropolarimeter, that will be available to the CFHT communities in 2015. SPIRou will be a unique tool for the study of cool dwarfs, and will be used to undertake an ambitious survey of habitable Earth-sized planets around nearby M dwarfs.

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.

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