Aluminum corrodes but it does not rust. Rust refers only to iron and steel corrosion.
Aluminum is actually very prone to corrosion. However, aluminum corrosion is aluminum oxide, a very hard material that actually protects the aluminum from further corrosion. Aluminum oxide corrosion also looks a lot more like aluminum, so it isn't as easy to notice as rusted iron.
When iron corrodes the color changes and it actually expands. This expanding and color change can produce large red flakes that we all know as rust. Unlike aluminum oxide, the expanding and flaking off of rust exposes new metal to further rusting. This why it is so important to provide a barrier so rust doesn't start.