Magnetic fields rule many physical processes in and around stars throughout their lifetime. All cool stars possess a magnetic field, likely generated by dynamo processes. In order to properly understand the evolution of cool stars, we need to understand their magnetism. Stellar magnetic fields can be directly observed through the imprint of the Zeeman effect in intensity and polarized spectra. In intensity spectra (Stokes I), spectral lines are broadened or split into several components by the magnetic field. Modelling this effect in high-resolution spectra allows us to determine the average unsigned magnetic field strength over the stellar surface. The magnetic field also induces circular (Stokes V) and linear polarization (Stokes QU) in spectral lines, according to its orientation. These polarization signals can be used to map the large-scale magnetic field at the surface of the star using tomographic techniques such as Zeeman Doppler imaging (ZDI). 

In this thesis, we investigated pre-main-sequence T Tauri stars and the active M dwarf AD Leo with the goal to understand their magnetic fields. We modelled the Zeeman broadening in high-resolution near-infrared spectra of low-mass and intermediate-mass T Tauri stars and derived their mean magnetic field strengths. In intermediate-mass T Tauri stars, we only found fields weaker than 2-3 kG. However, we found that low-mass T Tauri stars can have a wide range of magnetic field strength from relatively weak fields of 1.5 kG to fields as strong as 4.4 kG, and that their field strengths do not correlate with stellar parameters. Our observations of the M dwarf AD Leo led to the first detection of linear polarization in the spectral lines of an M dwarf. We also discovered that its Stokes V profiles, which were constant over many years, had changed in our observations. We mapped its global magnetic field using ZDI and found that it became concentrated into smaller areas on the stellar surface. Finally, we analyzed Stokes IV observations of the spectroscopic binary V1878 Ori. Both components of this system are intermediate-mass T Tauri stars with very similar properties. We determined stellar parameters by studying orbital motion of the components and comparing their disentangled spectra to theoretical models. We then mapped the global magnetic fields of the two stars simultaneously using ZDI. We found that their magnetic fields have radically different geometries and different strengths.