The study of the Cosmic Microwave Background (CMB) anisotropies is one of the key tools of Modern Cosmology. The most important limitations of the experiments aimed at measuring both the intensity and the polarisation of the CMB are the systematics and the foregrounds, i.e. the Milky Way diffuse emission. This thesis will be devoted to the characterisation of these two aspects, with particular regard to the Multi-Frequency Instrument (MFI) of the QUIJOTE (Q-U-I JOint TEnerife) experiment.

The MFI consists of four horns that can measure intensity and polarisation between 10 and 20 GHz at angular resolutions between 40’ and 57’. It has been operative almost continuously since November 2012, providing data of several calibrators, Galactic sources and extended fields for cosmological analyses. The first part of this thesis consists in the full characterisation of the optics of the MFI. The main beams are obtained through geostationary satellites observations and the results are confirmed with simulations and Cassiopeia A observations. We measure ellipticities > 0.92 and beam efficiencies > 0.90 in all horns. We estimate the level of the first sidelobe at -40dB at 11GHz, and the far sidelobes are found at a level of -70dB, which is unprecedented for a microwave experiment. The Müller matrices formalism is used to analyse the polarisation response of the instrument. The main contaminant to CMB observation is the intensity-to-polarisation leakage, which is below 1% at 11GHz in the MFI.

The major contaminants to the CMB polarisation are the synchrotron radiation and the dust emission of our Galaxy. The MFI is specifically designed to characterise the former type of emission, which is found mainly along the Galactic plane and in a region around the Galactic centre called Haze but can be found also at higher Galactic latitudes. In the second part of thesis we analyse ≈ 1300 hours of MFI data, covering four fields: W44, W49, W63 and the Haze. We produce the spectral energy distributions of 13 compact sources and adjust them with physical parameters that model the synchrotron, free-free and thermal dust emission. Also, a phenomenological model is used for the anomalous microwave emission, which has been found in 11 sources. The diffuse emission is studied in the Haze region. We found that its main component is free-free at low Galactic latitudes and synchrotron at b ≈ 8º. In polarisation, we measure a spectral index of -2.54 in temperature, which is in agreement with the Haze spectrum measured by Planck.