This thesis is dedicated to the study of the data from the first two instruments of the Q-U-I JOint Tenerife Experiment (QUIJOTE) experiment: the Multi Frequency Instrument (MFI) and the Thirty-and-Forty Gigahertz Instrument (TFGI). The MFI was installed at the Observatorio del Teide (OT) from 2012 to 2018, observing the sky between 10-20 GHz at degree scales. The TFGI has been installed at the OT since 2019, and observes the sky at 31 and 41 GHz with ~20 arcminute resolution.

A new parametric component separation method has been developed in order to retrieve the contribution from the emission components present in microwave spectra (synchrotron, free-free, anomalous microwave emission (AME), thermal dust and cosmic microwave background (CMB) anisotropies). This method has been focused on the analysis of intensity data, and was validated and extensively used during this thesis to recover the following science topics. It has also been parallelized to be used along with the IAC computing infrastructure.

The Wide Survey (WS) MFI data is used together with the previous method in order to recover maps for the parameters describing the CMB foregrounds signal along the Galactic plane (defined as the region with |b| < 10º). A total of ten maps, associated to the parameters describing the emission components previously cited, are recovered: the AME ones are discussed with greater detail. The AME peak frequency follows a Gaussian distribution with nu_AME = 20.7+2.0-1.9 GHz median value; the AME width in a log S_nu-log nu representation also follows a Gaussian distribution with median value W_AME = 0.560+0.059-0.050. Correlations have been found between the AME and thermal dust amplitudes; the best AME predictor is found to be the dust radiance, Rdust (SRCC= 0.95 ± 0.03). AME correlates more strongly either with small (a < 1 nm) or large (a > 10 nm) dust grains, than with intermediate ones (1 nm < a < 10 nm), which seem to be less likely to be the main AME carriers. The expected amount of AME in our Galaxy heavily decreases (even reaching a 50%) when MFI data is not introduced in the analyses, highlighting the importance of having data in this spectral region, as that provided by QUIJOTE-MFI.

MFI additional raster data is used together with that from the WS to study the Andromeda galaxy, or M31, to attempt to characterise a possible, now extragalactic, AME component. An AME component is found in M31 with significance larger than 3sigma. It is also shown that those models discarding such a component are less than 1% as favoured by the data as those considering AME. The AME emissivity is also computed, finding epsilon^28.4GHz_AME = 10.1±2.9 muK/(MJy/sr), fully consistent with that from our Galaxy computed within the previous analysis, epsilon^28.4GHz_AME = 11.6±3.5 muK/(MJy/sr). Furthermore, for the first time an upper constraint on the AME polarisation of an extragalactic object is computed, with Pi_AME < 40%.

Finally, the TFGI commissioning was performed with data acquired between November 2021 and October 2022, with 7 pixels installed in the instrument focal plane. The pointing model for the telescope was produced from planetary, Tau A and Cas A data, with accuracies better than 1 arcminute. Tau A data was also used to characterise the beams from the instrument pixels, showing FWHM values consistent with those expected: 22 and 18 arcminutes for those pixels observing at 31 and 41 GHz, respectively. Beam ellipticities were also compatible with the expected ones, with e < 0.1 values. A gain calibration model was produced from Tau A and Cas A observations. Large variations with time were detected, so data had to be calibrated independently by month. The uncertainty of this first model was estimated to be at least a 10%. Polarisation fractions, calculated from Tau A data, show remarkable agreement with previous works (6-7%) for two of the 31 GHz pixels. Instantaneous sensitivity estimates per channel have been obtained from Tau A observations, achieving 1.5-3 mK s^1/2 and 0.5-1 mK s^1/2 levels in intensity and polarisation, respectively. These translated into 150-300 muK s^1/2 and 60-100 muK s^1/2 sensitivities for the whole, 29-pixel detector array. Finally, first science and scientific validation observations were ran for the Cygnus and W44 regions. The maps for the first one show that the instrument recovers well the diffuse emission emission from the Galaxy, while achieving a polarisation sensitivity of ~20 muK/deg. The maps from W44 are used to verify that Aperture Photometry (AP) measurements performed on the brightest objects of the field (W43, W44 and W47) return consistent results with those from Wilkinson Microwave Anisotropy Probe (WMAP) and Planck, both in intensity and polarisation. The polarisation sensitivity computed for this field is 8-10 muK/deg. Both this value and the one for the Cygnus field suggest that the instrument is working as expect; it could achieve a 1 muK/deg sensitivity on a 1200-1300 deg^2 cosmological field after 3000 hours of observation while using the full 29-detector array.