Field theory is the mathematical language that we use to describe the deepest theories of physics

The most fundamental laws of nature that human beings have understood---the standard model of particle physics and Einstein's theory of gravity---are written in the language of field theory; quantum in the first case and classical in the second. The first field theory that you're likely to meet in your physics classes is electromagnetism, which describes the electric and magnetic fields through which light waves ripple all around us. But electromagnetism is actually fairly complicated; to learn field theory, it's better to start with a simpler example, and that's what I do in this video. I'll teach you the fundamentals using the Klein-Gordon theory of a real, scalar field. We'll see how to write down the Lagrangian, apply the principle of least action to obtain the Klein-Gordon field equation, how to solve it using plane waves, and how relativity is built in from the beginning. We'll also take a peek at quantum field theory along the way.