The paper describes the beginnings of the European monetary integration as the effect of world economy's globalization. Globalization is defined as a dominant tendency in the development of the world economy at the end of the millennium resulting in the formation of regional integration blocks, especially the triad America - Europe - Asia . Globalization of the monetary system leads to the creation of the monetary areas; one of the most formed ones is a Euro zone. The author characterizes the European Monetary Union as a unique phenomenon. He outlines its benefits (the decrease of the transaction costs, the elimination of the exchange rate risk, the increase of the price transparency) and the costs (the loss of the independent monetary policy, the loss of the exchange rate as an economic-monetary tool) and evaluates Euro as a specific tool of the integration with the Western European countries.