Create group Ctrl + number from 1-9
Center view on group Alt + number
Clear group Ctrl + 0
Zoom in/out + and -
Rotate viewpoint Mousewheel up/down or Ctrl + arrow keys
Take screenshot Ctrl + F12
Pause game Pause
Show/Hide Scores F4
Show/Hide Clock F11
Take full map screenshot Ctrl + Alt + F12
Review chat/announcements PageUp
Clear chat/announcements PageDown
Idle villager .
Idle military unit ,
Find hero /
Center view on selection Spacebar
Open chat dialogue Enter

Thanks for a commenter for finding these extras:

F1 - Unit Info window
F2 - Tech Tree
F3 - Show Objectives
F5 - Chat Window
F6 - Tribute Window
F7 - Diplomacy Window
F8 - Quick Save
F9 - Quick Load
F10 - Bring up Pause Menu (different from "Pause" key)

Ctrl + Up Arrow - Show Full UI
Ctrl + Down Arrow - Hide UI decorations

Stop Q
Attack move Alt + Right click or A + left click
Create unit waypoint Shift + Right click
Garrison selected units Alt + Right click on building/unit
Ungarrison N
Aggressive stance Alt + a
Defensive stance Alt + d
Stand ground Alt + s
Line formation Alt + l
Box formation Alt + b
Mixed formation Alt + m
Scattered formation Alt + x

Hoplite P
Hypaspist Y
Toxotes T
Peltast P
Hippikon C
Prodromos P
Petrebolos C
Helepolis R
Myrmidon
Hetairoi
Gastraphetes U
Archaic Age Hero A
Classical Age Hero S
Heroic Age Hero D
Mythic Age Hero F
Centaur C
Chimera I
Colossus O
Cyclops Y
Hydra H
Manticore M
Medusa D
Minotaur T
Nemean Lion N
Pegasus P
Scylla Y
Carcinos C
Argo O

Priest P
Mercenary I
Mercenary Cavalry C
Axeman A
Spearman S
Axeman A
Slinger L
Chariot Archer A
Camel C
War Elephant W
Siege Tower R
Catapult C
Anubite A
Avenger V
Mummy U
Petsuchos C
Phoenix N
Roc R
Scarab S
Scorpion Man M
Sphinx X
Wadjet W
Leviathan L
War Turtle U

Ox Cart N
Dwarf W
Hersir R
Ulfsark U
Throwing Axeman T
Raiding Cavalry C
Huskarl K
Jarl J
Portable Ram R
Ballista B
Battle Boar B
Einherjar E
Fenris Wolf W
Fire Giant F
Frost Giant G
Mountain Giant M
Troll T
Valkyrie V
Kraken K
Jormund Elver J

Arcus A
Argus R
Automaton A
Behemoth B
Caladria C
Destroyer D
Fanatic F
Fire Siphon S
Hekagigantes G
Katapeltes K
Lampades L
Murmillo M
Nereid N
Oracle O
Promethean P
Satyr S
Servant V
Turma T

name Build Find
Academy
Barracks
Longhouse B Ctrl + B
Archery Range A Ctrl + A
Armory R Ctrl + R
Dock D Ctrl + D
Farm F
Fortress
Migdol
Hill Fort
Palace V Ctrl + V
Granary
Guild G Ctrl + G
House
Manor E
Lighthouse L
Market X Ctrl + X
Mining Camp M Ctrl + M
Mirror Tower K Ctrl + K
Monument U Ctrl + U
Obelisk
O



Storehouse
Lumber Camp
Ox Cart
N

Ctrl + N

Siege Works C Ctrl + C
Stable
Counter-Barracks S Ctrl + S
Temple T Ctrl + T
Tower P Ctrl + P
Town Center Z H
Wall W
Wonder J