This might be a question best-suited for the Eastern Catholic forum, but I will attempt to provide a basic answer. The Union of Brest was an agreement signed in 1596 between Catholics and the so-called Ruthenian (or Ukrainian) Churches. Also called the Union of Brest-Litovsk, it should not be confused with the Treaties of Brest-Litovsk at the end of World War I. Through it, several million Ukrainian and Belorussian Orthodox Christians, residing under Polish rule, joined the Roman Catholic Church. Included in the union were the metropolitan of Kiev and the bishops of Ruthenia.
The union was organized through the expressed desire of Michael Ragoza, metropolitan of Kiev, and his leading bishops, to be united with the Catholic instead of the Orthodox Church. The Catholic king of Poland, Sigismund III, naturally encouraged the negotiations as a means of solidifying Catholic culture in the lands under his rule and to check Russian Orthodox religious influences in the region. He promised the Ruthenians that they could continue the traditional Eastern rite and they would have the same rights and privileges enjoyed by those Catholics of the Latin rite.
At a synod in Brest, the terms of the agreement were accepted by the Ruthenian bishops, Pope Clement VIII's approbation was given, and a union proclaimed. Unfortunately, the union was almost immediately challenged by some Ruthenian laypeople (many of whom who feared the inevitable Latinization of their liturgy and customs) and by several regional Orthodox bishops who were unwilling to accept the union. Russia also not surprisingly opposed the agreement, exerting much pressure on the Ukrainians and Belorussians to return to the Orthodox Church. Little help was given by Polish religious leaders, who looked down on the Ruthenians as second-class Christians. The result was that within a few years, many Ruthenians had returned to the Orthodox Churches after often violent confrontations. Nevertheless, the union was a significant milestone in the history of the Eastern Catholic Churches.
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