Language of the New Testament
The mainstream consensus is that the New Testament was written in a form of Koine Greek, which was the common language of the Eastern Mediterranean from the Conquests of Alexander the Great (335–323 BC) until the evolution of Byzantine Greek (c. 600).
The Hellenistic Jewish world 
The New Testament Gospels and Epistles were only part of a Hellenistic Jewish culture in the Roman Empire, where Alexandria had a larger Jewish population than Jerusalem, and Greek was spoken by more Jews than spoke Hebrew. Other Jewish Hellenistic writings include those of Josephus, Philo, Demetrius the chronographer, Eupolemus, Pseudo-Eupolemus, Artapanus of Alexandria, Cleodemus Malchus, Aristeas, Hecatus of Abdera, Thallus, and Justus of Tiberias, Pseudo-Philo, many Old Testament Pseudepigrapha and the Septuagint translation of the Hebrew Bible itself.
Background on Koine Greek 
Whereas the Classical Greek city states used different dialects of Greek, a common standard, called Koine (κοινή "common"), developed gradually in the 4th and 3rd centuries BC as a consequence of the formation of larger political structures (like the Greek colonies, Athenian Empire, and the Macedonian Empire) and a more intense cultural exchange in the Aegean area, or in other words the Hellenization of the empire of Alexander the Great.
In the Greek Dark Ages and the Archaic Period, Greek colonies were founded all over the Mediterranean basin. However, even though Greek goods were popular in the East, the cultural influence tended to work the other way around. Yet, with the conquests of Alexander the Great (333-323 BC) and the subsequent establishment of Hellenistic kingdoms (above all, the Seleucid Empire and Ptolemaic Kingdom), Koine Greek became the dominant language in politics, culture and commerce in the Near East.
During the following centuries, Rome conquered Greece and the Macedonian Kingdoms piece for piece until, with the conquest of Egypt in 30 BC, she held all land around the Mediterranean. However, as Horace gently puts it: "Conquered Greece has conquered the brute victor and brought her arts into rustic Latium" (Graecia capta ferum victorem cepit et artis intulit agresti Latio.) Roman art and literature were calqued upon Hellenistic models.
Koine Greek remained the dominant language in the eastern part of the Roman Empire, extending into the Byzantine Empire as Byzantine Greek. In the city of Rome, Koine Greek was in widespread use among ordinary people, and the elite spoke and wrote Greek as fluently as Latin. Jewish Koine Greek did not exist as a separate dialect, but some Jewish texts in Koine Greek do show the influence of Aramaic in syntax and the influence of Biblical background in vocabulary.
Languages used in ancient Palestine 
After the Babylonian captivity, Aramaic replaced Biblical Hebrew as the everyday language in Palestine. The two languages were as similar as two Romance languages or two Germanic languages today. Thus Biblical Hebrew, which was still used for religious purposes, was not totally unfamiliar, but still a somewhat strange norm that demanded a certain degree of training to be understood properly.
After Alexander, Palestine was ruled by the Ptolemies and the Seleucids for almost two hundred years. Jewish culture was heavily influenced by Hellenistic culture, and Koine Greek was used not only for international communication, but also as the first language of many Jews. This development was furthered by the fact that the largest Jewish community of the world lived in Ptolemaic Alexandria. Many of these diaspora Jews would have Greek as their first language, and first the Torah and then other Jewish scriptures (later the Christian "Old Testament") were therefore translated into standard Koine Greek, i.e. the Septuagint.
Currently, 1,600 Jewish epitaphs (funerary inscriptions) are extant from ancient Palestine dating from 300 B.C. to 500 A.D. Approximately 70 percent are in Greek, about 12 percent are in Latin, and only 18 percent are in Hebrew or Aramaic. "In Jerusalem itself about 40 percent of the Jewish inscriptions from the first century period (before 70 C.E.) are in Greek. We may assume that most Jewish Jerusalemites who saw the inscriptions in situ were able to read them".
The language of the New Testament 
Most biblical scholars adhere to the view that the Greek text of the New Testament is the original version. An opposite view, that it is a translation from an Aramaic original (recently called "Aramaic primacy") has not gained popularity. At any rate, since most of the texts are written by diaspora Jews such as Paul of Tarsus and his possibly Gentile companion, Luke, and to a large extent addressed directly to Christian communities in Greek-speaking cities (often communities consisting largely of Paul's converts, which appear to have been non-Jewish in the majority), and since the style of their Greek is impeccable, a Greek original is more probable than a translation.
Even Mark, whose Greek is heavily influenced by his Semitic substratum, seems to presuppose a non-Hebrew audience. Thus, he explains Jewish customs (e.g. Mark 7:3-4, see also Mark 7), and he translates Aramaic phrases into Greek (Mark 3:17: boanerges; Mark 5:41: talitha kum; Mark 7:34: ephphatha; Mark 14:36: abba; Mark 15:22: Golgotha; Mark 15:34, see also Aramaic of Jesus and Sayings of Jesus on the cross). In the Aramaic Syriac version of the Bible, these translations are preserved, resulting in odd texts like Mark 15:34:
- Greek text
καὶ τῇ ἐνάτῃ ὥρᾳ ἐβόησεν ὁ Ἰησοῦς φωνῇ μεγάλῃ· ελωι ελωι λεμα σαβαχθανι; ὅ ἐστιν μεθερμηνευόμενον Ὁ θεός μου ὁ θεός μου, εἰς τί ἐγκατέλιπές με;
- Syriac text (with rough transliteration)
ܘܒ݂ܰܬ݂ܫܰܥ ܫܳܥܺܝܢ ܩܥܳܐ ܝܶܫܽܘܥ ܒ݁ܩܳܠܳܐ ܪܳܡܳܐ ܘܶܐܡܰܪ ܐܺܝܠ ܐܺܝܠ ܠܡܳܢܳܐ ܫܒ݂ܰܩܬ݁ܳܢܝ ܕ݁ܺܐܝܬ݂ܶܝܗ ܐܰܠܳܗܝ ܐܰܠܳܗܝ ܠܡܳܢܳܐ ܫܒ݂ܰܩܬ݁ܳܢܝ܂
wbatša‘ šā‘yin: q‘ā’ yešua‘ bqālā’ rāmā’ we’mar, ’ēl ’ēl lmānā’ šbaqtāni di’aiteyh ’elāhi ’elāhi lmānā’ šbaqtāni
- King James
"And at the ninth hour Jesus cried with a loud voice, saying, Eloi, Eloi, lama sabachthani? which is, being interpreted, My God, my God, why hast thou forsaken me?"
In the Peshitta:
- Mark 7:34 does not contain the doubled-up meaning.
- Mark 15:34 have two versions of the same expression: the former in Jesus's spoken dialect, the latter in another dialect
Languages of Jesus 
The languages spoken in Galilee and Judea during the first century include the Semitic Aramaic and Hebrew languages as well as Greek, with Aramaic being the predominant language. Most scholars agree that during the early part of first century Aramaic was the mother tongue of virtually all natives of Galilee and Judea. Most scholars support the theory that Jesus spoke Aramaic and that he may have also spoken Hebrew and Greek. Stanley E. Porter concluded: "The linguistic environment of Roman Palestine during the first century was much more complex, and allows for the possibility that Jesus himself may well have spoken Greek on occasion."
Other views 
Critics of the mainstream consensus in favour of Greek being the original language of the New Testament claim logical improbabilities in the Greek Text compared to the Syriac/Hebrew Texts and vocabulary containing wordplay in the Syriac/Hebrew New Testament texts that parallels Hebraic wordplay in the Old Testament.
- Kurt Aland, Barbara Aland The text of the New Testament: an introduction to the critical 1995 p52 "The New Testament was written in Koine Greek, the Greek of daily conversation. The fact that from the first all the New Testament writings were written in Greek is conclusively demonstrated by their citations from the Old Testament, .."
- Archibald Macbride Hunter Introducing the New Testament 1972 p9 "How came the twenty-seven books of the New Testament to be gathered together and made authoritative Christian scripture? 1. All the New Testament books were originally written in Greek. On the face of it this may surprise us."
- Wenham The elements of New Testament Greek -p xxv Jeremy Duff, John William Wenham - 2005 "This is the language of the New Testament. By the time of Jesus the Romans had become the dominant military and political force, but the Greek language remained the 'common language' of the eastern Mediterranean and beyond, and Greek ..."
- Daniel B. Wallace Greek Grammar Beyond the Basics: An Exegetical Syntax of the New Testament 1997
- Henry St. John Thackeray Grammar of New Testament Greek ed. Friedrich Wilhelm Blass, 1911 "By far the most predominant element in the language of the New Testament is the Greek of common speech which was disseminated in the East by the Macedonian conquest, in the form which it had gradually assumed under the wider development ..."
- David E. Aune The Blackwell companion to the New Testament 2009 p61 CHAPTER 4 New Testament Greek Christophe Rico "In this short overview of the Greek language of the New Testament we will focus on those topics that are of greatest importance for the average reader, that is, those with important ..."
- Joseph Mélèze-Modrzejewski The Jews of Egypt: from Rameses II to Emperor Hadrian
- Hor., Epist. 2. 1. 156–7
- Pieter W. Van Der Horst, "Jewish Funerary Inscriptions - Most Are in Greek," Biblical Archaeology Review, Sept.-Oct. 1992, p. 48.
- The International Standard Bible Encyclopedia p281 ed. Geoffrey W. Bromiley - 1959 "Almost all scholars agree that our Gospel of Matthew was originally written in Greek and is not a translated document. Matthew's Greek reveals none of the telltale marks of a translation."
- F. F. Bruce The New Testament Documents
- James Barr, Which language did Jesus speak, Bulletin of the John Rylands University Library of Manchester, 1970; 53(1) pages 9-29 
- Handbook to exegesis of the New Testament by Stanley E. Porter 1997 ISBN 90-04-09921-2 pages 110-112
- Discovering the language of Jesus by Douglas Hamp 2005 ISBN 1-59751-017-3 page 3-4
- Jesus in history and myth by R. Joseph Hoffmann 1986 ISBN 0-87975-332-3 page 98
- James Barr's review article Which language did Jesus speak (referenced above) states that Aramaic has the widest support among scholars.
- Porter, Stanley E. (2004). Criteria For Authenticity In Historical-jesus Research. Continuum International Publishing Group. p. 164. ISBN 978-0-567-04360-3. Retrieved 16 May 2013.
- Jung, Chang-Wook (2004). The Original Language of the Lukan Infancy Narrative. Continuum International Publishing Group. pp. 13–15. ISBN 9780567082053.
- LeRoy Culbertson, Philip (1995). A Word Fitly Spoken: Context, Transmission, and Adoption of the Parables of Jesus. SUNY Press. p. 226. ISBN 9780791423110.