To start producing stone, you need a Stone Quarry.
This building costs 3 Coins.
Though stone is not used in conversion, it is essential in building special buildings, such as Houses.
Tile Factory
In the "Tile Factory" you can produce Clay, as well as convert Clay to produce Bricks and eventually Pottery.
This building costs 4 Coins.
Obtaining Bricks is beneficial for building special buildings, such as Houses and making Pottery (which can be exchanged for Coins in some of the Houses).
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"A Stone Quarry produces Stone blocks that are essential for the construction of any settlement's buildings."
"This building produces Clay that is used to make Bricks. They can also be transformed into Pottery."