Inventions of the Dark Age

History books, at least those that cover the period, shed lots of tears about the fall of Rome, and call the next 1000 years the Dark Ages.  Starting with Gibbon (Decline and Fall)  most historians treat the medieval period as a huge setback to civilization with no redeeming features.  Perhaps.
   Dark they might have been, but the medievals were inventive.  In the thousand years we call medieval, they invented a lotta good stuff.  What they didn't invent they imported from elsewhere and placed it into service.

1.  Trebuchet.  Weight driven catapult, powerful enough to break a masonry wall, something which the spring driven catapults of the Greeks and Romans could not do.
2.  Wooden barrels.  Shipping container that completely replaced the heavy and fragile pottery amphora used in antiquity.  Stronger and lighter than pottery
3.  Magnetic Compass.  The odds of your ship returning safely are much better if she carries a compass.
4.  Stern rudder.   Much stronger and less likely to break in heavy weather than the steering oar.  Moderns who have sailed replica vessels of antiquity (Thor Heyerdahl and Hodding Carter) always write about their steering oar breaking at sea.
5.  Spectacles (eye glasses)
6. Stirrups.  Without stirrups, it's like riding bareback.  You can do it, but you have to pay all your attention to staying on the horse.  With stirrups the horseman's seat is firm enough to fight effectively.  With stirrups the mounted knight, who dominated European warfare, becomes possible.
7. Heavy plow.  A big strong plow, often wheeled, with an eight ox team, which could turn the heavy bottomland soil, which the lighter "ard" used in antiquity could not.
8.  Three field rotation.  Let only one third of the land lie fallow, as opposed to the two field rotation practiced in antiquity.  Increases cropland by one sixth (17%)
9. Water mills.  Although a Roman invention, the Romans never built very many of them.  Whereas the Domesday book records 5 to 6 thousand water mills in England by 1087
10.  Blast furnace.  Water wheel powered bellows made a fire hot enough to actually melt iron, so that it could be poured and cast in molds.
11. Printing.  Gutenburg and all that.
12. Gunpowder. and firearms.
13. The University.
14. Crossbow.  Although known to the Romans (there is an engraving of one on a Roman tomb) it wasn't used much.  Major advantage of the crossbow; it is as simple to shoot as a modern rifle.  Any recruit could be trained to shoot well enough to be useful in a few weeks.  The long bow took a lifetime of practice to make an archer. 
15. Spinning Wheel
16.  Mechanical clock.
17.  Gothic  cathedral
18.  Horse collar.  Before the horse collar, law limited the load horses could pull to 500 pounds.  With horse collars medieval wagoneers could move 2500 pound loads of building stone.
19. Windmill
20. Arabic numerals
21. Double entry book keeping.
22. Scientific method  (Roger Bacon)
23. Wheel barrow.  Simple, but highly useful.