When do you use the Monopoly development card? Before or after rolling the dice? Please explain why using the official rules.
Assuming you're referring to the "Monopoly" development card in Catan (aka The Settlers of Catan), then the official FAQ at Catan.com answers this:
Development Cards in General - May I play Development Cards before rolling the dice?
Yes. Note that you may play only 1 Development Card per turn: if you have played this card before rolling the dice, you are not allowed to play another one afterwards.
So you may play Monopoly before or after rolling the dice. Strategically, it usually makes sense to play it later, since most of the time rolling the dice gives people more cards for you to take, and playing Monopoly before making trades will probably mean people won't want to trade with you. (And, of course, there's the classic move of making a large number of trades for a resource, then playing the Monopoly to take all of those cards back from everyone. It's a move that generally only works once.)