Buildings facilitate unit production, can increase income and improve governmental control within a province. The cost of construction is displayed in the bottom left and the time required is shown in the bottom right of the picture.
Left-click on a building to add it to the construction queue, and again to remove it. When you select a castle or a building elsewhere in a province (such as a port or farm), the construction tab will appear. The majority of buildings are clustered around the daimyo's castle - the whole settlement being known as a 'castle town' (or 'settlement' in Fall of the Samurai).
