What is the difference between single and double coil? How exactly do they work? What is the differences with the cover no cover thing?

I was going to search for this but it would have just brought up a ton of threads...and it would take a couple days just to see if there was a thread about this already...
Double coil pickups (more commonly known as humbuckers) produce much less feedback than single coils, and have more of a warm tone than the bright tone of single coils
A single coil is the type of pickup you would see on a Stratocaster, for example. Single coils are also on Telecasters and other guitars, too. It has a thinner, brighter tone and is really good in country, blues, and pop settings. A double coil, or, as it is better known, a humbucker, is basically two single coils put together, and is seen on Les Pauls, Explorers, and various other guitars. It has a thicker, warmer sound than the single coil and is good in blues, rock, and jazz settings. Really, though, you could use either pickup in pretty much any style of music. As for the difference with or without a cover, it depends on what you hear when you compare the two. In his Bluesbreaker days, Eric Clapton took the pickup covers off of his Les Paul because he felt that it raised the output slightly. Try with and without pickup covers to decide what you like best.
"Notes are expensive. . .use them wisely"-B.B. King

"It's been very important throughout my career that I've met all the guys I've copied, because at each stage they've said, 'Don't play like me, play like you."-Eric Clapton