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Li-llāhi ʼabū-ka is an expression of praise, meaning "to God is attributable [the excellence of] your father".
As a verb, ʼ-b-w means "to become [as] a father to [somebody]" (ʼabawtu) or "to adopt [him] as a father" (ta'abbā-hu or ista'bā-hu).
Abu may be used as a kunya, an honorific. To refer to a man by his fatherhood (of male offspring) is polite, so that ʼabū takes the function of an honorific. Even a man that is as yet childless may still be known as abū of his father's name, implying that he will yet have a son called after his father.
The combination is extended beyond the literal sense: a man may be described as acting as a father in his relation to animals, e.g., Abu Bakr, "the father of a camel's foal"; Abu Huraira, "father of kittens". In some cases, a man's enemies will refer to him in such a way to besmirch him, e.g. Abu Jahl, "the father of ignorance". A man may be described as being the possessor of some quality, as Abu'l Gadl, "father of grace", or "the graceful one"; Abu'l Fida, "father of devotion", or "the devout one". An object or a place may be given a nickname, such as Abu'l hawl, "father of terror", (the Sphinx at Giza). Abu'l fulus, "father of money", is frequently used to refer to a place where rumors have been told of a treasure being hidden there.
Pirke Avot (Hebrew: פרקי אבות, Chapters of the Fathers) ' are a Mishnaic tractate of Avot, the second-to-last tractate in the order of Nezikin in the Talmud. The tractate of Pirkei Avot is dealing with ethical and moral principles.
The word ’Abba came to be applied as a title of honor to the rabbis in the early centuries of the Common Era and is found as such in the Babylonian Talmud. (Berakhot 16b) The one acting in the capacity of vice-president of the Jewish Sanhedrin already held the title of ’Av, or Father of the Sanhedrin. In later periods the title was also applied to the bishops of the Coptic, Ethiopic, and Syrian churches and, more particularly, became the title of the Bishop of Alexandria. The English words “abbot” and “abbey” are both derived from the Aramaic ’abba. Jerome, the translator of the Latin Vulgate, objected to the use of the title “abbot” as applied to the Catholic monks in his time and did so on the basis that it violated Jesus’ instructions at Matthew 23:9: “Moreover, do not call anyone your father on earth, for one is your Father, the heavenly One.”
A transliteration of the Aramaic term abba also appears three times in the Greek New Testament of The Bible. Each time the term appears in transliteration it is followed immediately by the translation ho pater in Greek, which literally means “the father.” In each case it is used with reference to God. Mark records that Jesus used the term when praying in Gethsemane shortly before his death, saying: “Abba, Father, all things are possible to you; remove this cup from me. Yet not what I want, but what you want.” (Mark 14:36) The two other occurrences are in Paul’s letters, at Romans 8:15 and Galatians 4:6. It seems evident from these texts that, in apostolic times, the Christians made use of the term ’Abba in their prayers to God.
Abba is sometimes translated in sermons as "daddy",  which has been rejected by most scholars because abba, unlike "daddy", was used by adult children as well as young children.  Indeed, the usage of abba in Galatians 3:22-4:7 suggests that abba "asserts not childlike relation to God, but the privileged status of the adult son (not daughter) and heir". 
The name Barabbas in the New Testament comes from the Aramaic phrase Bar Abba meaning "son of the father".
Av (Hebrew: אָב, Standard Av Tiberian ʾĀḇ Aramaic אבא Abba; from Akkadian abu; "father" ; plural: Hebrew: אבות Avot or Abot) means "father" in Hebrew. The exact meaning of the element ab (אב) or abi (אבי) in Hebrew personal names (such as Ab-ram, Ab-i-ram, Ah-ab, Jo-ab) is a matter of dispute. The identity of the -i- with the first person pronominal suffix (as in Adona-i), changing "father" to "my father", is uncertain; it might also be simply a connecting vowel. The compound may either express a nominal phrase (Ab[i]ram = "[my] father is exalted") or simply an apposition (Ab[i]ram = "father of exaltedness"). Forms with the connecting vowel and with the pronominal suffix were likely confused, so that the translation will depend on what is meaningful in connection with the second element.
See also 
- Hebrew name
- Mama and papa
- Ibn, an Arabic particle meaning "son" used to form names
- Ben (Hebrew), a Hebrew particle meaning "son" used to form names
- James Barr, "Abba isn't 'daddy'", Journal of Theological Studies, 39:28-47.
- Mary Rose D'Angelo, "Abba and 'Father': Imperial Theology and the Jesus Traditions", Journal of Biblical Literature, Vol. 111, No. 4 (Winter, 1992), pp. 615-616
- Tarazi, Fr. Paul. THE NAME OF GOD: ABBA. Word Magazine - Publication of the Antiochian Orthodox Christian Archdiocese of North America (May 1980) pp. 5-6. http://www.orthodoxresearchinstitute.org/articles/bible/tarazi_name_of_god.htm