The Catholic Church is a communion of churches sui iuris, which means "of their own law." These churches are fully in communion with the Pope in Rome but retain their own distinct liturgical, theological, spiritual, and canonical traditions. Here is an overview of the Catholic Churches sui iuris and the Catholic communion of churches:
 

I. Catholic Churches Sui Iuris
 

1.  Latin Church (Roman Catholic Church):

The largest of the sui iuris churches.

Uses the Roman Rite, among others (like the Ambrosian and Mozarabic Rites).

Headquarters in the Vatican City.

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2. Eastern Catholic Churches:

These churches follow various Eastern Christian liturgical traditions and are in full communion with the Pope.

They are grouped into several liturgical families:

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Byzantine Rite:

 

• Ukrainian Greek Catholic Church: The largest of the Eastern Catholic Churches.

• Melkite Greek Catholic Church.

• Ruthenian Greek Catholic Church.

• Romanian Greek Catholic Church.

• Italo-Albanian Catholic Church.

• Greek Byzantine Catholic Church.

• Slovak Greek Catholic Church.

• Hungarian Greek Catholic Church.
   

Alexandrian Rite:

• Coptic Catholic Church.

• Ethiopian Catholic Church (including the Eritrean Catholic Church).

Antiochene (West Syrian) Rite:

• Maronite Church.

• Syriac Catholic Church.

• Syro-Malankara Catholic Church.
   

Armenian Rite:

• Armenian Catholic Church.
   

Chaldean (East Syrian) Rite:

Chaldean Catholic Church.

Syro-Malabar Catholic Church.

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II.  Catholic Communion of Churches

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The Catholic Church is a communion of these 24 autonomous (sui iuris) churches, which are united by their common faith, shared sacraments, and communion with the Pope. Key aspects of this communion include:

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1. Unity of Faith: All churches in the Catholic communion share the same core doctrines, including belief in the Trinity, the divinity of Jesus Christ, the sacraments, and the authority of the Pope.

2. Diversity of Traditions: Each sui iuris church maintains its own liturgical rites, theological emphases, spiritual practices, and canonical traditions. This diversity enriches the universal Church.

3. Papal Primacy: The Pope, as the Bishop of Rome, is recognized as the spiritual leader and highest authority in matters of faith and morals. His role is to maintain the unity and orthodoxy of the Church.

4. Synodality and Autonomy: While in communion with the Pope, each sui iuris church has its own governance structures, often led by a patriarch, major archbishop, or metropolitan, and exercises a significant degree of self-governance

5. Inter-Church Relations: The different sui iuris churches often work together on pastoral, educational, and charitable activities, respecting each other’s traditions and contributing to the global mission of the Catholic Church.

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In summary, the Catholic Church is a rich tapestry of 24 sui iuris churches, each with its unique heritage, united under the leadership of the Pope and sharing a common faith.