The Standard Model (SM) has been confirmed by many precision tests to be one of the greatest achievements of modern physics. However, it is not the ultimate theory since there are many remaining questions that cannot be explained, including the existence of dark matter, the flavor structure, the origin of matter-antimatter asymmetry and the neutrino masses. These unexplained questions motivate us to explore new physics beyond the SM (BSM) while being consistent with the existing experimental data.

The Higgs discovered at the LHC provides a new window to explore the BSMs. In the SM, the scalar sector is constructed in the simplest way using one scalar doublet. Extensions with an extra singlet, doublets as well as triplets are widely investigated to accommodate the aforementioned questions. Symmetries play an important role in particle physics as providing the necessary mathematical system. For instance, the SM is based on the gauge group SU(3)C ⊗ SU(2)L ⊗ U(1)Y. So adding proper symmetry can not only make the new model more structural but also reduce the number of free parameters. In this dissertation, we explored the new physics from the Three-Higgs-Doublet model with S3 symmetry subject to several constraints from the existing measurements: fermion masses, CKM matrix, PMNS matrix, neutron electric dipole moment (nEDM) and bounded from below (BFB) conditions. We found the new model can fit into the current data while predicting that there will be another eight heavier Higgs bosons out there to be discovered. Also, we predict the effective neutrino mass in beta decay, effective Majorana neutrino mass in neutrinoless double beta decay, summation of neutrino mass in cosmology, the masses of the new Higgs bosons and the neutron EDM value corresponding to the lowest heavy Higgs boson. Although the new Higgs bosons are too heavy to be tested in the current collider, the neutron EDM value can be used as an indirect signal.