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Gems from exploration give you additional "raw resources" when you found your next city. Water and iron are the raw resources, giving you some materials and food without having to build anything. Gems can also show up as a raw resource, giving you gold.

A save string isn't a bad idea, but I don't intend to continue development on this game. It could be used in a sequel though.

You'll need to bump up your research levels for that building first. Click the Research button at the top and then click on the building you want to be able to upgrade. Of course this takes another resource, Science.