Gauge theories are the underpinning theories that we use to understand the fundamental forces and how they interact with particles. Originally constructed under physical concepts and notation and now using the geometrical language of fibre bundles, we can mathematically model such interactions. A lot of literature on this topic tends to preference either the physical formulation or the mathematical formulation. In my talk, I will provide an explanation of gauge fields, gauge potentials and gauge transformations using both physical motivation and mathematical formulation to draw clearer lines between fibre bundles and physical definitions. There will be particular focus on classical electromagnetism (and its interaction with charged particles) and the classical Yang-Mills field.