Studies on $H\rightarrow b\bar{b}$ decay and $VH$ production with the ATLAS detector

The ATLAS experiment physics program can be summarized into two goals: the test of the Standard Model and the search for Beyond the Standard Model (BSM) physics signatures. Both aspects are tackled in this thesis as the first part of the work is dedicated to the measurement of the Higgs boson decay to a couple of b-quarks as predicted by the SM, while another part addresses the search for deviations in the Higgs boson production and decay in a phase space highly sensitive to BSM effects. In this thesis, the Higgs boson decay into two b-quarks is studied in the associated production with a vector boson ($W$ or $Z$) decaying into leptons. Two complementary strategies have been developed and they are indicated as resolved and merged analysis. In the resolved analysis the Higgs boson decay products are reconstructed as two separate objects (b-jets) while in the merged analysis, designed for the high energy phase space, the two b-jets produced by the highly boosted Higgs boson tend to coalesce and are reconstructed as a single large jet. The resolved analysis search led to the first observation of the Higgs boson decay into two b-quarks and to the first observation of the VH production. The data sample used for the $H\rightarrow b\bar{b}$ search has also been used to perform measurements of the VH cross-section in bins of the V-boson transverse momentum. This measurement, exploiting the so-called Simplified Template Cross Section framework, is designed to investigate possible BSM effects.