A Lumber Hut is a building that produces 1 population to the city its built in. It can only be placed on forest tiles, and it can only be placed after Forestry is researched. Each Lumber Hut costs 2 stars.
The Sawmill, which is unlocked after researching Mathematics, produces 1 extra population to the city which it is built in for every adjacent lumber hut, even if the lumber hut is in another one of your cities' territories.
The Sawmill can be upgraded to a max level and produce a lot of population