Here are some books which have been recommended here in the past. It is in no way exhaustive of the possibilities, so recommend other books if you have one in mind.
Light For Life
Part One: The Mystery Believed
Part Two: The Mystery Celebrated
Part Three: The Mystery Lived
The Eyes Of The Gospel: Introduction To The Spirituality of the Eastern Church by Archbishop Joseph Raya
Byzantine Church and Culture by Archbishop Joseph Raya
The Face of God by Archbishop Joseph Raya
Are We All Schismatics? (Or, We Are All Scismatics) by Archbishop Elias Zoghby
Anything from
Madonna House Publications
A Voice From the Byzantine East by Archbishop Elias Zoghby
American Eastern Catholics by Fred Saato
Introduction to Eastern Christian Spirituality: The Syriac Tradition by Chorbishop Seely Beggiani
Captivated By Your Teachings by Father Anthony Salim
The Lord’s Prayer and/or Beatitudes by St. Gregory of Nyssa
The Triads by St. Gregory Palamas
The following books are all available through
Theological Book Service and have facilitator guides available. If one of these is chosen, I could see about getting an experienced facilitator to lead us through the book.
Stream of Living Water: An Introduction to Holy Tradition
Life and Worship: An Introduction to Eastern Theology
Shown to be Holy: An Introduction to Eastern Moral Thought
To the Ends of the Earth: Aspects of Eastern Catholic Church History
With Eyes of Faith: An Introduction to Eastern Theology
Inexhaustible Delights The Holy Mysteries in the Byzantine Churches
The Old Testament: A Byzantine Perspective
The Holy Gospel: A Byzantine Perspective
The Apostolic Writings: A Byzantine Perspective