The proposal that light energy travels in discrete quanta rather than continuous waves, and what that explains about the photoelectric effect.
How the random jittering of tiny particles suspended in a liquid follows from the motion of unseen molecules, and how it can be measured.
How measurements of time and distance depend on the observer's motion, and why the speed of light is the same for everyone.
The argument that a body giving off energy loses mass, and that mass and energy are therefore two measures of the same thing.