I'm looking to learn about Air Motion Transformer technology

An air motion transformer is like an accordion. It has a pleated diaphragm that squeezes air out of the pleats when it vibrates so very little vibration will produce a lot of air motion. Just another way of matching impedance with air. They are easy to make as tweeters and will go down lower than most dome tweeters. Some of them run as low as 500 Hz. They will also go very loud. It is much harder to make a woofer with this technology but I think people are working on it. If you go to Parts Express you can see that there are many of them for sale and most are cheap. They have also been around since the 70's. My experience with them is very limited. The high end speaker industry has mostly avoided them for some reason preferring dome tweeters.  

Thank you mijostyn!  This is a great start for me.

AMT's are great designs IF you pay some attention to one thing. It is by far best for sound quality if the Diaphragm Former is made, as it usually is in any good design, from a silk material. The Former provides the physical support structure for the diaphragm material. It is meant to be as audibly transparent as possible and in fact has to be in order to do its job without resonating itself and adding its own coloration to the sound. The silk-derived Former is recognizable from its gray/whitish fibrous appearance, fairly semi-opaque or semi-translucent looking, although in some designs this might not be visible until the tweeter is disassembled. 

The problem is that some companies that make cheaper ATM's (often Chinese) use Kapton for the Former material. It's visibly a red colored plastic material and is pennies to produce. But, Kapton is not Nearly as audibly transparent as any silk-derived material and will noticeably color the sound, at least up to about 10kHz or so at which point it seems to no longer be resonating...but anything below that point is trouble.

Just avoid anything that advertises using Kapton and look for those ATM's that mention silk and you should be fine. This will bump up the price range your looking in, but it will be the difference between an ATM that lives up to its promise vs one that plainly doesn't.

In general, ribbon tweeters may sometimes have that last nth degree of uber detail or resolution compared to ATM's, but not by much at all. The difference may only make it a little easier to blend ATM's with the mid or woofer compared to ribbon. Ribbons tend to "beam" vertically more than ATM's - another thing that makes for easier driver integration for ATM's. 

Ribbons by design have the ribbon itself that is replaceable. It needs to be replaceable because it can get stretched if played too loud, at which point it can lose performance or even break. The cost of a new ribbon is much cheaper than the cost of a new tweeter.  ATM's don't have this problem, but they can take SPL's similar to ribbons without damage...but if you go Too far, you'll need to replace the whole tweeter - but, that's mostly only a problem if you're a metalhead or something :>)