In this thesis we have studied three independent tools to get information on cosmological parameters: the large scale structure (LSS) of matter in the Universe, galaxy clusters and the cosmic microwave background (CMB).

In the study of the LSS we have provided an analytical recipe for computing the conditional mass function (CMF), i.e. the mass distribution of the halo abundance in overdense and underdense regions. We have considered a formalism already discussed in the literature and introduced an additional parameter to ensure the CMF normalisation. We have compared the predicted halo abundance from this CMF recipe with the one obtained from numerical N-body simulations, for conditions with Eulerian radii from 5 to 30 Mpc/h, and for halo masses between 10^(11) and 10^(14) M_sun/h. We have found excellent agreement with simulated abundances in underdense regions at all scales, and in overdense regions at large scales; we have also confirmed that the CMF normalisation is satisfied at all scales. We have finally presented an analytical fit to the matter-to-halo bias function in underdense regions, which could be of special interest to speed-up the computation of the halo abundance when studying void statistics. This fit is capable of reproducing the computed halo bias with an error below 2% for the reference cosmology, and below 9% when considering different values of redshift and sigma_8.

With respect to the cosmology with galaxy clusters, we have considered the abundance of clusters as a function of redshift as a tool to estimate the cosmological parameters Omega_m and sigma_8. We have implemented the computation of the cluster redshift distribution according to a specified cosmology, and developed a statistical tool based on a Markov Chains Monte Carlo (MCMC) method to retrieve the cosmological parameters starting from the cluster abundance. We have applied our code to the cosmological subsample of the PSZ1 catalogue of clusters detected by the Planck satellite with signal-to-noise ratio above seven. We have obtained estimates of Omega_m and sigma_8 based on the cluster abundance in combination with BBN and BAO likelihoods, considering the bias 'b' in the determination of the cluster mass as a fixed or free parameter.  With the bias parameter fixed to the value b=0.2 we found Omega_m=0.293±0.020 and sigma_8=0.760(+0.018,-0.017) (68% C.L.). With 'b' free to vary with a flat prior in the range [0.0,0.3] we found Omega_m=0.289(+0.022,-0.020) and sigma_8=0.750±0.028. These results are in very good agreement with the ones obtained by the Planck Collaboration using the same cluster catalogue. This proves the reliability of our method, that can therefore be applied in the future to broader catalogues, resulting in a significant reduction of the error bars in the estimation of these parameters. An example is the extended cosmological subsample of the PSZ1, that contains nearly three times the number of clusters employed for the analysis in this work and that will soon be made publicly available.

We have employed the Sunyaev-Zel'dovich effect as a cosmological probe. To this aim we computed the one dimensional probability distribution function (PDF) of the Compton parameter 'y' measured by the Planck satellite over the whole sky; this PDF is strongly dependent on the parameter sigma_8. We have modelled the galaxy cluster contribution to the PDF and tested our formalism with simulated Compton parameter maps. We have applied this formalism to fit for sigma_8 against the PDF extracted by Planck data. We have considered only values for
y>4.5*10^(-6) in order to leave out contamination from instrumental noise and other astrophysical foregrounds, and obtained the final estimate sigma_8=0.77±0.02 (68% C.L.). This result is compatible with other cluster-based estimates, and shows a tension with the value obtained from CMB analysis (~0.83). This tension may be due to systematics in the modelling or instrumental calibration or it can be the first hint for a necessary extension of the standard cosmological model.

The study related to the CMB presented in this thesis is based on the QUIJOTE experiment, and on the data obtained with the multi-frequency instrument (MFI). We have carried out the pointing calibration of the first QUIJOTE telescope, developing a set of coordinate transformations to correct for the telescope non-idealities: these transformations have been implemented in the MFI data reduction pipeline and are routinely employed to achieve a pointing correction with errors below 1 minute of arc. We have considered observations of the MFI in the galactic regions W49, W51 (molecular clouds) and IC443 (supernova remnant), and assessed the relative contribution of different emission mechanisms. In particular, we have found hints of detection of anomalous microwave emission (AME) in intensity in all regions, with a higher significance in W49. We have also detected synchrotron emission in the regions W49 and IC443. This information is relevant for modelling the synchrotron emission properties in our Galaxy, and this way making the separation of the cosmological B-modes signal easier in future data from this and other experiments.