Lorentz condition for potential and gauge theory

Hello there, im new and don't have any background in field theory such as gauge theory etc.. i knew that in maxwell's eq, there are called Lorentz's condition... and when i want to probe it for more detail, i encounter the gauge theory... so my question is, what direction should i follow in order to understand Lorentz's condition and what is the physics branch should i focus in order to understand field... is it gauge field theory?

Sorry if this topic already exist..
Thanks