What are the rules of settling?

I'm pretty new to Civilization, but I'm getting the hang of the rules I think. Recently, I had a settler and was going to have him create a city in this narrow strip land, but was told I couldn't settle a city within 4 spaces of another city. I interpreted that as "not within 4 spaces of the boundary of ANY city (even other players)... but I think I got that wrong because Russia just settled a city right on my border... so can anyone explain what specifically is meant by this rule?

Also, is there anyway to stop Russia's settler without going to war with them?