Etymology of Theology
Theology is the study of religious belief and God. It is also a system of ideas and beliefs that deals with God and other religious questions.
Protagoras, a Greek philosopher, was critical of theology (and got exiled from Athens because of it). He believed that one cannot know whether the gods exist or not, or what form they might possess.
We start with Hellenistic Greek and the word theologia (θεολογία). The first part of this word, theo (θεό) is a bound morpheme of theos (θεός), which means God or god or goddess. The second part, logia (λογία), means theory or study of or branch of study or science. Many of our English words use logia in some way or another, such as biology and psychology.
Theologia, therefore, literally means the study of God or the study of the gods.
This Ancient Greek word eventually evolved into the Latin theologia, which evolved into the Old French, Middle French and Middle English theologie. From theologie we forged the modern English word, theology.
Theology in Other Languages
Barnhart, Robert K., ed., Barnhart Dictionary of Etymology, H.W. Wilson Co., 1988.
de Vaan, Michiel, Etymological Dictionary of Latin and the other Italic Languages, Alexander Lubotsky ed., Leiden: Brill, 2008.
Lewis, Charlton T., Elementary Latin Dictionary, Oxford, 1890.
Licoppe, Guy. Modern Latin. Calepinus Novus.
Liddell, Henry George, and Robert Scott, eds., Intermediate Greek-English Lexicon, Oxford Univ. Press, 1883.
McSparran, Frances, chief editor, The Middle English Compendium, University of Michigan, 2006.
The Oxford English Dictionary, 2nd ed., Clarendon Press, 1989.