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A currency is a "means of payment" or "medium of exchange" that is in circulation and is generally used and accepted by the public or between different countries or governments. It is basically the specific kind of money that is officially used by or pertains to a certain country. The euro, for example, is the currency that pertains to and is used in the Eurozone.
The means of payment are generally in the form of coins, cash (paper money), cheques, transfers, digital money (like the crypto-currency Bitcoin, among others), etc. and are demoninated in one specific currency.
The value of currencies fluctuates because they are tradeable or exchangeable on the worldwide money markets and, therefore, exchange rates are created to match the value of one currency to another based on many differente economic variables. The main variables that make currencies fluctuate are: