Medieval technological advances.

   The middle ages invented or imported a lot of new stuff.  Far more than the preceding ancient world did.  The last invention made in the ancient world was the discovery of iron working by the Hittites 600 or 700 BC.  The Roman Empire at its peak, say 200 or 300 AD, did not have any technology that the Hittites did not have 800 or 900 years before.  That is a long time for stasis.

   The Middle Ages start after the fall of the Roman Empire and last until Columbus time.  We date the end of the Roman Empire with the deposition of Romulus Augustilus in 470 something AD and Columbus is 1492.  You can round it off and say the Middle Ages run from 500 to 1500 AD, a thousand years.  In that time Europeans invented or imported the following:

1. Trebuchet, a stone throwing machine powerful enough to break stone walls.  It was a weight driven machine, replacing classic catapults, which were powered by skeins of springy materials, perhaps human hair.  Unfortunately the art of making such skeins and keeping them springy has been lost since ancient times.  Trebuchets can be built on site from local timber and some rocks for weight. 
2. Magnetic compass.  We think this was an import from China.  Having a compass on board your ship greatly improved the chances of said ship returning safely from voyages.
3. Wheelbarrow.  Very simple device that greatly improves the amount of stuff that one man can move.
4. Wooden kegs and barrels.  They replaced the clay amphora used as shipping containers in classic times.  Lighter and more rugged than amphora which were just big clay pots.
5. Gunpowder and the fire arms to use it.
6. Lenses and eyeglasses.
7. Stern rudder.  Far stronger than the classical steering oar and less likely to break off in bad weather.
8. Printing.
9. Cast iron.  Classical black smiths only had wrought iron. 
10. Crossbow.  Powerful and accurate.  Although known in classic times it was only used for hunting.  You could train any man to shoot a crossbow well in a matter of weeks.  Robin Hood’s long bow, although effective, required a bowman to start shooting as a child and practicing every day all his life.  The supply of good bowmen was limited.
11.  Water mills.  Although known in classic times, the middle ages made much greater use of watermills.  The Domesday Book, William the Conqueror’s inventory of all the land and buildings in England, lists better than a thousand water mills in England by 1080 AD.
12. Horse collars.  Far more effective horse harness that greatly improved the amount of stuff a horse could move.