Magíster en Ciencias, Mención Astronomía / In this thesis I present a search for MgII absorption systems in the resolved spectra of 10 high redshifts gravitationally lensed quasars. The goal of the thesis is to study the spatial structure of MgII systems. The quasars were observed at resolutions $R\sim4\,500$ and $R\sim40\,000$. The search yielded a sample of 31 MgII absorption systems at $0.4<z<1.6$ and probing transverse separations between lines of sight (LOS) in the range 0.29-23 $h^{-1}_{70}$ kpc. Adding systems from the literature increased the number of systems to 95. The range of transverse separation of the full sample is 0.3-100 $h^{-1}_{70}$ kpc. In this sample, the dispersion in the fractional equivalent width differences, $\Delta W_r$, decreases with equivalent width for strong systems while no high $\Delta W_r$ values are found for transverse distances $d<9$ $h^{-1}_{70}$ kpc. This is in agreement with a smooth distribution of gas at these scales. In addition, these systems show a trend of increasing $\Delta W_r$ with transverse separation. For weak systems, the dispersion in $\Delta W_r$ with respect to $W_r$ is greater than for strong systems. In this case anticoincidences (i.e., absorption in just one LOS) are found homogeneously in the range $0.2-30$ $h^{-1}_{70}$ kpc. For coincidences, $\Delta W_r$ increases with transverse separation but after $3-4$ $h^{-1}_{70}$ kpc the trend reverses. These results indicate that weak systems are more patchy or smaller than strong ones. To estimate transverse sizes, I have used two likelihood methods. The first one considers the absorption systems as spheres or disks with a uniform distribution of gas. This method yields $R\sim$ $10$ and $14$ $h^{-1}_{70}$ kpc for weak and strong systems, respectively. The second likelihood method uses the individual equivalent widths and assumes the equivalent width varies with impact parameter, i.e. $W_r=W_r(r)$. For $W_r(r)$, I tested a power law and a logarithmic function. The logarithmic function seems to be in better agreement with the data for both strong and weak systems. The second method yields $R\sim$ 20 and 40 $h^{-1}_{70}$ kpc for weak and strong systems, respectively. Thus, both methods yield smaller sizes for weak population. These sizes are much smaller than estimates using just the frequency of systems, $\frac{dN}{dz}$. Combining the results of models and observations suggests that size estimation of strong MgII systems is consistent with the assumed distribution of gas, while for weak systems the resulted sizes from the likelihood analysis seem to be overestimated. In conclusion, weak systems are predicted to be smaller ($3-4$ $h^{-1}_{70}$ kpc) and more patchy than strong systems.