Theology is the study of God.
The History of God
One of the best History I enjoy of the concept of God and the sacred is Karen Armstrong's 2009 The Case for God.
The transcendence of God indicates that he is beyond any concept, language or experience. He cannot be limited or contained. A literal description of God is nothing but an idol, however- sophisticated that mental idol might be.
But if God is infinite, there is no place where he may not be found, so there is no way to experience him without simultaneously experiencing something else as well. He is therefore described as immanent - found within everything.
Proof of Existence of God
This topic is covered in a number of books which cover ontological, cosmological and teleological arguements for God, In general the conclusion I have come to is that you have difficulty in getting agreement on the definition of God. Obvious the definition will determine what it is that you are attempting to establish.
When I was younger the question seemed important. Today, I am more interested in the toipic of spirituality.
Science and Theology
God, Sin and the Problem of Evil
If God is Omnipotence (All Powerful) and Omniscience (All knowing) and All loving why does he, she permit evil, pain and suffering.
The classical catorization of sin and evil have today almost been entirely abandoned.
The Relationship between God and Religion
 Thompson, Mel (2007) Teach Yourself Philosophy of Religion, New York: McGraw Hill Ryerson
Adler, Mortimer (1980) How to Think About God, Toronto: Bantam Books
Armstrong, Karen (2000) The Battle for God, New York: Ballantine Books
Armstrong, Karen (2009) The Case for God, New York: Alfred A Knopf
Bailey, Andrew (2004) First Philosophy: Fundamental Problems in Philosophy, Volume 1 Values and Society
Bultmann, Rudolf (1958) Jesus Christ and Mythology, New York: Charles Scribner
Cavey, Bruxy (2007) The End of Religion, Colorado Springs: Navpress
Dawkins, Richard (2006) The God Delusion,Boston: Houghton Mifflin Company Ehrman, Bart D. (2008) God's Problem, How the Bible Fails to Answer Our Most Important Question-Why We Suffer,New York: Harper Collins
Hauser, Marc D.(2006) Moral Minds, The Nature of Right and Wrong, New York: Prennial Harper
Hinde Robert A.(2002) Why Good is Good, The Source of Morality New York: Routledge
Hodgson, Peter C. and Robert H. King (1982, 1985) Christian Theology, An Introduction to Its Traditions and Tasks, Revised and Enlarged Edition
Hunnex, Milton D (1986) Chronological and Thematic Charts of Philosophies & Philosophers, Grand Rapids: Zondervan Publishing House
Knight, Christopher(2001) Wrestling with the Divine, Religion, Science, and Revelation
McGrath, Alister and Joanna Collicutt McGrath (2007) The Dawkins Delusion? Atheist Fundamentalism and the Denial of the DevineDowwners Grove, Illinois: IVP Press
Russell, Bertrand (1957) Why I am Not A Christian, New York:George Allen & Unwin Ltd
Sullivan, Deidre (1990) What do we Mean When We Say God?, New York: Cader Books Doubday
Sweetman, Brendan (2007) Religion, Key Concepts in Philosophy, New York: Continuum
Thompson, Mel (2007) Teach Yourself Philosophy of Religion, New York: McGraw Hill Ryerson
Tillich, Paul (1967) Systematic Theology, Chicacgo: The University of Chicago Press
Vosper, Gretta (2008) With or Without God, Toronto: HarperCollins Publishers Wright, Robert (2009) The Evolution of God, New York: Little Brown and Company