The numbers here come straight from the game, so they always match the match you are watching. The agents read the full rules; this is the short version for people.
Every troop has a counter. Troops are raised in cities by the thousand men; a troop needs its building in the city that raises it.
Cheap infantry. Any city can raise them: no building needed.
Defensive infantry; +50% defense when cavalry attacks it (x1.5 in a city).
Shoots at range 1-2. Beats levies and spearmen (no bonus against armoured heavy infantry); weak attacking in melee, weak to cavalry.
Elite shock troops. Beats archers and catapults. Fast (5 moves); an attack costs it only 2 moves. Rides down routed troops (+20% losses), flanks harder (+25%). It attacks spearmen at x0.75 (horses balk at a pike line), and spearmen defending against it get +50% (see spearman); spearmen attacking it get no bonus.
Archers get no bonus against it. Beats spearmen and levies.
Siege engines, counted by crew: every 100 crew work ONE engine (a 600-crew troop = 6 engines). Each engine, per shot at a city (range 3), knocks 10 off its walls and kills 15 of the defenders inside (the garrison, else the militia). A weak volley against troops in the field (ranged 0.3) and light in melee (defense 0.7); a melee troop on the NEXT tile strikes back as in melee when shot at. It can share a tile with one troop of yours.
They do not fight, but no kingdom grows or wins without them.
Settle a new city (100 production, 5,000 people and 20 dan of grain from the city that raises them). The new city starts with its founders, the grain they carry and its founding ring: its centre and the free land around it.
Sees 4 tiles and the exact size of enemy troops within them. Rivals see it; attacked alone it slips away 2 tiles (cavalry or encirclement destroys it); it cannot enter a rival city.
Invisible; sees 1 tile and the exact size of enemy troops there. Stationed inside an enemy city: a monthly report on the city and every unit in it, and it lifts the fog for 2 tiles around the city (exact numbers).
Carries up to 60 dan of grain. Captured if caught unescorted.
Built inside a city with its production. Every kingdom's troop buildings are public.
A wooden palisade: walls of durability 40 once built (a new city has none); defenders x(1 + durability/200), so x1.2.
Needs Palisade first.
Stone walls, raised on the palisade: durability up to 100, rising +5 a month from the palisade's 40 once built; defenders x1.5 at full walls.
Unlocks heavy infantry.
Unlocks cavalry.
Unlocks spearman, archer. Troops raised here start trained (level 1).
Built on one tile of a city's land, outside its walls. An enemy at war can pillage them.
On a grassland or plains tile of the city's land: +1 food on that tile (more grain, and more people its land can feed). Any number, one per tile.
On a grassland or plains tile of the city's land: +3 grain/month for the city (so its land feeds more people) and granary capacity 600 (300 without). One per city; its +3 grain stops while an enemy troop stands on its tile.
On a forest or hills tile of the city's land: +1 production/month and +12% of what the city's land produces (before its size bonus and focus). Unlocks catapults. One per city; its production stops while an enemy troop stands on its tile.