Civil Disorder

Welcome to CFC.
Disorder happens when the number of unhappy citizens in a town is higher that the number of happy citizens. So you need to make them happier; raise the luxury rate at the Domestic Advisor screen, acquire more luxuries, or create specialists.
If the unhappiness is caused by war-weariness you can cure that by making peace, if possible.
 
Certain buildings improve city happiness as well: Temples, Colosseums, and Cathedrals. Build Temples as you need them, skip the Colosseums, and build Cathedrals if you are taking your cities above size 12.

The quickest (and I believe best) method of making your peeps happy is to hook up a luxury resource on the map and connect all cities by roads/railroads, and especially your Capital. Examples are furs (they look like beavers on the map), ivory (elephants), spices, etc etc - you can find the full list in the in-game Civilopedia and can usually find at least one luxury within distance of your starting location.

EDIT: here's a link to the list of luxuries http://www.civfanatics.com/civ3/resources/#luxury
 
If you have at least three luxuries, marketplaces also make citizens happier. As I recall, the Civilopedia details how much extra happiness the marketplace gives for each extra luxury. As I recall, it works precisely like this: Let M stand for marketplace, and accordingly M(x) indicate the amount of extra contentedness one gets from x luxuries via the marketplace. Then,
M(1)=0
M(2)=0
M(3)=1
M(4)=2 (one for the 3rd luxury and one on top of that for the 4th luxury)
M(5)=4 (two for the 5th luxury)
M(6)=6
M(7)=9 (three for the 7th luxury)
M(8)=12

If I recall correctly, you can derive this from the happy faces on the city screen. The first happy face on the same line as the luxury indicates increased happiness/contentedness from the luxury itself. All other happy faces indicate extra happiness/contentedness gained from the marketplace. So, with a marketplace, the number of happy faces H seen next to the xth luxury goes
H(1)=1
H(2)=1
H(3)=2
H(4)=2
H(5)=3
H(6)=3
H(7)=4
H(8)=4

So, M(x)=M(x-1)+H(x)-1, with M(1)=0. Thus,
M(2)=M(1)+H(2)-1=0+1-1=0
M(3)=M(2)+H(3)-1=0+2-1=1
M(4)=M(3)+H(4)-1=1+2-1=2
M(5)=M(4)+H(5)-1=2+3-1=4
M(6)=M(5)+H(6)-1=4+3-1=6
M(7)=M(6)+H(7)-1=6+4-1=9
M(8)=M(7)+H(8)-1=9+4-1=12
 
questions on luxuries - Do two or more of the same lux give you more happy citizens, or is the benefit limited to one? And, if I have only one of a lux and trade it, do I lose it? Maybe you don't trade unless you have at least two?
 
Do two or more of the same lux give you more happy citizens, or is the benefit limited to one?

You do not get any additional benefit from having two of the same luxury. The only reason to hook up a second luxury of the same type is to open up trading possibilities. It also opens you up to demands, though.

if I have only one of a lux and trade it, do I lose it?

Yes.

Maybe you don't trade unless you have at least two?

You can trade your only luxury of one type, which may be advantageous. If you have a small empire, you may be able to trade one luxury for 2 or 3 luxes.
 
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