In this chapter, we embark on a comprehensive exploration of gauge field theory, that leads us to the Standard Model of particle physics framework. We begin by investigating Abelian, then non-Abelian symmetries, particularly SU(2) and SU(3), which underpin the electroweak and strong interactions, respectively. Our journey brings us to study historical aspects and deepens with a rigorous examination of the Higgs mechanism, a pivotal concept elucidating how gauge bosons acquire mass through spontaneous symmetry breaking. This mechanism completes the electroweak theory and provides profound insights into the origins of particle masses. We meticulously construct the Standard Model Lagrangian, revealing the intricate interplay between gauge fields, fermionic matter, and the Higgs field. Through this mathematical framework, we uncover the underlying structure of the fundamental forces governing particles and their interactions, showcasing the Standard Model’s remarkable predictive power in describing the dynamics of our universe at the most fundamental levels.