Inside menu :

Navigate : WASD
Select : Numeric keypad [1]
Back : Numeric keypad [2]

In-game :

Move : WASD
Rotate left : Q
Rotate right : E
Previous player : Numeric keypad [4]
Next player : Numeric keypad [5]
Quick access to a hero : 1, 2, 3, 4
Use right hand : Numeric keypad [1]
Use left hand : Numeric keypad [2]
Inventory : Numeric keypad [0]
Use life potion : Numeric keypad [6]
Use mana potion : Numeric keypad [3]
Action / Pick up : Space
Sleep : Z
Map : Tab
Menu / Discard a healing spell : Esc
Quick Save : F5
Quick Load : F9

Inventory :

Navigate : WASD
Previous player : Numeric keypad [4]
Next player : Numeric keypad [5]
Quick access to a hero : 1, 2, 3, 4
Select : Numeric keypad [1]
Equip / Use / Unequip : Numeric keypad [0]
Drop : Space
Close : Numeric keypad [2]

Pick up window :

Previous player : Numeric keypad [4]
Next player : Numeric keypad [5]
Quick access to a hero : 1, 2, 3, 4
Take : Numeric keypad [1], left mouse click
Equip : Numeric keypad [0], right mouse click
Next item if more than one, if only one close the dialog : Space
Close the pick up dialog : Numeric keypad [2]

You can exchange items between players by clicking on a player portrait with an item selected.
You can also sleep by clicking on the Zzz button at the top right corner.

Inside menu :

Navigate : D-Pad
Select : A
Back : B

In-game :

Move : D-Pad
Rotate left : LB
Rotate right : RB
View : Right stick
Previous player : LT
Next player : RT
Use right hand : A
Use left hand : B
Inventory : Y
Action / Pick up : X
Use life potion : Left stick up
Use mana potion : Left stick down
Sleep : Right stick button
Map : View
Menu / Discard a healing spell : Menu

Inventory :

Navigate : D-Pad
Previous player : LT
Next player : RT
Select : A
Equip / Use / Unequip : Y
Drop : X
Close : B

Pick up window :

Previous player : D-Pad left
Next player : D-Pad right
Take : A
Equip : Y
Next item if more than one, if only one close the dialog : X
Close the pick up dialog : B

You can exchange items between players clicking on a player portrait with an item selected.
You can also sleep clicking the Zzz button on the top right corner.