The turbine engine is actually very simple to understand, if you took the components I talked about in this video and assembled them you could actually have yourself a functional turbine. The only hard part would be getting the air to fuel ratio correct so it can be self sustaining. There are actually people that build their own jet engines from scrap material in their garage. Here is a video showing a fully functional version.
https://www.youtube.com/watch?v=jje0wV4l0tM
Here are the three different types of turbine engines.
The turbojet was the first to be invented and is the main topic of this page. But there needed to be a more efficient engine than this for commercial flight so the turbofan was built.
The turbofan is the same concept as the turbojet but with less compressor blades and one big fan blade at the front of the engine creating most of the thrust. This method is the most efficient of the three engines and therefore its used on all planes today.
The turboprop is a turbofan engine but with a geared prop at the front. This is used on helicopters and propped planes today. I say it is geared because right behind the propeller is a gear box that allows the prop to spin slower than the engine. It this prop were to spin at the same RPMs as the engine than it would tear itself apart.