Conservation of energy is simply the invariance of a system to translation in time: the system shows the same time evolution from a well defined starting state regardless of whether that state exists at a time t or a time t+t' with an arbitrary t'. This is one application of Noether's theorem.

This is an example of a topic that unstructured self study would likely skip. But it is included in every properly structured course because this theorem puts a fundamental explanation to all conserved quantities that occur in classical mechanics.