Eastern Catholic Churches

The Catholic Church is compromised of 24 sui iuris (autonomous or self-governing) churches, each with its own hierarchy, traditions, and discipline, but united under the the Pope. 

The liturgical traditions or rites presently in use in the Church are the Latin (principally the Roman rite, but also the rites of certain local churches, such as the Ambrosian rite, or those of certain religious orders) and the Byzantine, Alexandrian or Coptic, Syriac, Armenian, Maronite and Chaldean rites. In "faithful obedience to tradition, the sacred Council declares that Holy Mother Church holds all lawfully recognized rites to be of equal right and dignity, and that she wishes to preserve them in the future and to foster them in every way." 

The celebration of the liturgy, therefore should correspond to the genius and culture of the different peoples. In order that the mystery of Christ be "made known to all the nations... to bring about the obedience of faith, "it must be proclaimed, celebrated, and lived in all cultures in such a way that they themselves are not abolished by it, but redeemed and fulfilled: It is with and through their own human culture, assumed and transfigured by Christ, that the multitude of God's children has access to the Father, in order to glorify him in the one Spirit.

- Catechism of the Catholic Church
Article 2: Liturgical Diversity and the Unity of the Mystery, para 1203 & 1204

These 24 churches (1 Latin Rite & 23 Eastern Rites) are all in communion with one another, are all within the Catholic Church and all recognize the primacy of the pope.