In 431 b. c. sparta and other city-states joined forces against athens to fight this war with who?

Well I believe you may have answered your own question there. In 431 B.C., the Peloponnesian wars took place. An altogether nasty business they were. If you'll allow me to delve into a brief history lesson, the two city states of Athens and Corinth were always on sour terms, but they signed a treaty that said they wouldn't kill each other. Unfortunately, as per usual with these things, the treaty didn't last. 

Another city state, Corcyra, decided one day to settle a small town of Epida*nus. Sadly, Epida*nus was constantly attacked by its neighbors and Corcyra had too much on its plate to help out poor Epida*nus. So, Epida*nus called out to Corinth to help them out, and Corinth agreed. Well, Corcyra didn't like Epida*nus getting all buddy buddy with Corinth, so eventually tensions boiled over and Corcyra and Corinth declared war.

Corcyra started losing the war however, so the sent a plea to Athens to help them out. Corinth told Athens that if they helped Corcyra out, the treaty would be broken. Athens decided to help anyway. Soon more city states joined the fray and now you have all out war, with Athens, Corcyra and others fighting against Corinth, Sparta and others.

Hope this helps :)