I am wanting to study what the Easter Orthodox believe concerning soteriology, what book would be best fit for that study?
I'm not really sure the Eastern Orthodox think in terms of Western theological concepts such as soteriology. Theirs is a more mystical theology. Their whole goal is not "salvation" as we in the West would think of it, but "deification" or "theosis." But you might find something close to what you're looking for in Elements of Faith: An Introduction to Orthodox Theology, particularly in Chapter 8 (Jesus Christ), section i ("Ransom" and "Redemption").
There's a good chapter on "The Deification of Humanity – Theosis" in Eastern Orthodox Christianity: A Western Perspective by Daniel B. Clendenin. A couple of key excerpts:
Orthodox theology in the East likewise places the questions of human destiny, sin, and salvation at the forefront of its entire theological vision, albeit in ways very different from the Western Christian tradition. The long history of Orthodox theology answers the question of the purpose of life with a definitive, unique, and unified response. It is a response that not only is different from Western conceptions of theological anthropology, but also sounds very strange indeed to our ears.
...
It is not too much to say that the divinization of humanity is the central theme, chief aim, basic purpose, or primary religious ideal of Orthodoxy. Theosis is the ultimate goal towards which all people should strive,4 “the blessed telos for which all things were made.”5 In emphasizing this doctrine Orthodox theologians focus on more than what the Theoretikon identifies as the purpose of life; for Orthodoxy, deification is “the very essence of Christianity,” for it involves the “ineffable descent of God to the ultimate limit of our fallen human condition, even unto death—a descent of God which opens to men a path of ascent, the unlimited vistas of the union of created beings with the Divinity.”6 To paraphrase Athanasius, when God descended, assumed humanity, and was “incarnated,” he opened the way for people to ascend to him, assume divinity, and become “in-godded.” In its very definition of the gospel, then, Eastern Christianity presupposes the idea of deification; even when the term is not explicitly mentioned, it is implicitly present “as the content of the salvation proclaimed by the gospel.”7
Clendenin, D. B. (2003). Eastern Orthodox Christianity: A Western Perspective (2nd ed., pp. 119–121). Grand Rapids, MI: Baker Academic.
I did a search of orthodox NEAR soteriology with Match all Word forms checked, and it seems there is quite a bit people like to write/discuss about Orthodox thinking on soteriology. I found quite a few references, without knowing specifically what you might be looking for, they all had some interesting points. Just a few to consider:
Deification in Eastern Orthodox Theology
Salvation as Praxis: A Practical Theology of Salvation for a Multi-Faith world
Historical Theology in-depth: Themes and Contexts of Doctrinal Development Since the First Century
Justification: Five Views
Eastern Orthodox Theology: A Contemporary Reader
The best thing we currently have in Logos format (live products) is Andrew Louth's book Introducing Eastern Orthodox Theology, and specifically the chapters titled "Who is Christ?," "Sin, Death, and Repentance," and "Being Human—Being in the Image of God."
Another one is:
Beyond Salvation: Eastern Orthodoxy and Classical Pentecostalism on Becoming like Christ
It has a substantial section on "The Incarnation and Soteriology" in Chapter 2 which is on Orthodox Theologians and Theosis.
