to clarify, this machine is way less impressive than what a lot of media claim it is. the greeks had hundreds of years of stargazing and records to figure out a model of the cosmos, and this is basically their whole model in a mechanism. unfortunately, at the time this thing was made, their model was pretty far off and they couldn't come up with a better one due to philosophical reasons (the earth is the center! the orbits of the planets must be some sort of perfect circles!).

anyway, this thing is somewhat impressive technically, but is really bad in terms of engineering:

• the teeth of the gears are triangular. there is a part of the mechanism that is super elaborate and calculates very precisely the motion of the moon and how it slows down and speeds up occasionally, but because of the triangular teeth, whether or not this actually worked is debatable.
• the mechanism used crown gears, which are pretty bad because they don't mesh well with the regular gears.
• some of the gears are put under a lot of strain, particularly gear d1, a small gear that sits at the end of the gear chain b2 -> c1 -> c2 -> d1 (which gets faster and faster)
• the mechanism has a lot of spacers soldered into place and rivets that were hammered in, making disassembly rather difficult. however some of the components are fastened in by pins.
• the main gear b1 (the large one with the cross spokes you see in the picture) was built in a very weird way: the gear itself is a ring, and the spokes are added on later, connected to the ring with dovetail joints which aren't the easiest thing to make when your level of tech is a file and some sandpaper. in fact, whoever made the mechanism probably screwed up one of the joints and had to rivet in an extra metal plate so it wouldn't fall off.
• the gear trains for the moon is built in a very weird way: first the main axis b drives 2 separate gear trains that pass through the main plate, only for one gear train to drive a turntable (e3 and e4) and the other to drive a shaft (e2 and e5) that goes through the center of the turntable. e5 will then drive a mechanism on the turntable which has an output shaft... that once again goes through the center of the turntable and the e2-e5 shaft (e1 and e6). then finally e1 drives b3, which drives a shaft that goes right through the center of the b axis. so now, you have 3 pairs of gears on the e axis whose shafts all go through each other like some matryoshka doll, as well as a hole right through the b axis to display the position of the moon.
• the metonic and saros spirals on the back need resetting once in a while, because the pointers move in spirals and can't automatically reset once they hit the end.

we knew that the greeks had a model of the cosmos before we discovered this (i think). we also knew, from greek records, that there were people discussing about "spheres" that tracked the positions of the planets, sun and moon as they moved through the sky. the main thing this mechanism shows is that the ancient greeks possibly pioneered complex gear mechanisms, and the knowledge was then passed on and on and went through times like the islamic golden age before coming back to europe in the form of clockwork and watchmaking.