Rockets- How they fly in Space

I have always wondered how rockets could fly in space, as we all know oxygen is needed for combustion, but there is no oxygen is space. So I researched about this topic, and came up with some interesting results.
I found out that in a rocket's engine, a fuel propellant is burned with an oxidizer propellant to produce large volumes of very hot gas. The hot gas that is ejected from the rocket engine acts as a propellant, and produces thrusts for the rocket, to make it move. The hot gases that are ejected from the engine expand accelerates them until they rush out of the back of the rocket at extremely high speeds, propelling the rocket forwards. During takeoff, however, the rocket makes use of its liquid hydrogen and oxygen tanks to boost themselves out of the Earth's gravitational field.