Some suggestions on reading up on a few things… The works herein listed regarding the Orthodox Church are given because it is same faith professed by Eastern Christians.
Byzantine Catholic Faith
Each Sunday we recite the Creed also called the symbol of faith which, as you know, is a summary statement of Catholic Faith. Often we mindlessly rattle off the words not giving a a second thought of what passed our lips. Perhaps we can change that experience with understanding the Creed a little better. The Ruthenian Archeparchy (Pittsburgh) has provided the faithful with this article to provide a good, reliable summary of the articles of the Creed according to the Byzantine tradition.
Andrew Louth, Introducing Eastern Orthodox Theology, IVP Academic, 2013.
John Anthony McGuckin, The Eastern Orthodox Church: A New History, Yale University Press, 2020.
Eastern Christians and Their Churches by Fr. Steven Hawkes-Teeples, S.J., is a very fine and brief introduction taking the reader through the various liturgical traditions that constitute the Christian East. This is a must read. Fr. Hawkes-Teeples is a former professor at the Pontifical Oriental Institute (Rome) and the author of several works. While he is a Jesuit priest he also serves in a Byzantine Catholic parish in St. Louis, MO.
Timothy (Kallistos) Ware, The Orthodox Church: An Introduction to Eastern Christianity, Penguin Books, Penguin Books; 3rd Revised edition, 2015.
Joseph Raya, Byzantine Church and Culture, Madonna House Publishing, 1992.
Joseph Raya, Abundance of Love: The Incarnation and Byzantine Tradition, Madonna House Publishing; Third edition edition, 2016.
The Melkite Church
Raji Al Bdeiwi, The Particular Law of the Greek-Melkite Catholic Church, Valore Italiano, 2020.
(A personal translation as a research proposal for the doctorate in Eastern Canon Law from the Pontifical Oriental Institute, Rome. It is an unofficial translation of Melkite canon law.)
Elias Chacour with Mary E. Jensen, We Belong to the Land: The Story of a Palestinian Israeli Who Lives for Peace and Reconciliation, University of Notre Dame Press, 2001.
Serge Descy, The Melkite Church, Sophia Press, 1993.
Patriarch Gregory III (Laham), Introduction to Liturgical Services and their Symbolism in the Melkite Church
Lucien Malouf, Byzantine Melkite Thinking, Technogravure et Presse Libanaises, 1972.
Saba Shofany, The Melkites at the Vatican Council II: Contribution of the Melkite Prelates to Vatican Council II, 2005.