Razing and rebuilding
A city can either be razed when you win a battle over an enemy city. Razing it in this situation is free. You can also raze a city that you are already the owner of. To raze a city you need a unit in the city. Select the unit and click orders->raze in the top menu. This will bring up the raze window stating the cost to raze your city.
The cost to raze a city us calculated by the following formula:
5*city income + 25% * production value, however the min cost to raze is always 150 gold.
To rebuild a razed city you need to place a unit in the city with construction ability and then select orders->rebuild city in the top menu. The cost to rebuild is based on the following formula:
5*income + 500 gold.
Razing production in your city costs 25% of what it costs to buy.