The MiniBooNE experiment at the Fermi National Accelerator Laboratory (Fermilab) was designed to search for electron to muon neutrino oscillations at Delta m^2~1 eV^2 using an intense neutrino flux with an average energy of about 700 MeV. From 2002 to 2009 MiniBooNE has accumulated more than 1.0x10^{21} protons on target (POT) in both neutrino and antineutrino modes. MiniBooNE provides a perfect platform for detailed measurements of exclusive and semiinclusive neutrino cross-sections, for which MiniBooNE has the largest samples of events up to date, such as neutral current elastic (NCE), neutral current pi^0, charged current quasi-elastic (CCQE), charged current pi^+, and other channels. These measured cross-sections, in turn, allow to improve the knowledge of nucleon structure. This thesis is devoted to the study of NCE interactions. Neutrino-nucleus neutral current elastic scattering accounts for about 18% of all neutrino interactions in MiniBooNE. Using a high-statistics, high purity sample of NCE interactions in MiniBooNE, the flux-averaged NCE differential cross-section has been measured and is being reported here. Further study of the NCE cross-section allowed for probing the structure of nuclei. The main interest in the NCE cross-section is that it may be sensitive to the strange quark contribution to the nucleon spin, Deltas, this however requires a separation of NCE proton from NCE neutron events, which in general is a challenging task. MiniBooNE uses a Cherenkov detector, which imposes restrictions on the measured nucleon kinematic variables, mainly due to the impossibility to reconstruct the nucleon direction below the Cherenkov threshold. However, at kinetic energies above this threshold MiniBooNE is able to identify NCE proton events that do not experience final state interactions. These events were used for the Deltas measurement. In this thesis MiniBooNE reports the NCE (n+p) cross-section, the measurement of the axial mass, MA, and the Deltas parameter from the NCE data.