Who Is the Holy Spirit?
Question

In the Quran in 2:87, an excerpt: ...We gave Jesus the son of Mary clear (signs) and strengthened him with the Holy Spirit. What is the Holy Spirit?
Praise be to Allah.Who is the ‘Holy Spirit’ in the Quran?
The “Holy Spirit” (Ruh al-Qudus) is Jibril (peace be upon him). Shaykh al-Shanqiti said: “The words of Allah (interpretation of the meaning), ‘and [We] supported him with Ruh al-Qudus’ [al-Baqarah 2:87] refer to Jibril according to the most sound view. This is indicated by the words (interpretation of the meaning): ‘Which the trustworthy Ruh has brought down’ [al-Shu’ara 26:193] and ‘then We sent to her our Ruh’ [Maryam 19:17].”
Ibn Abi Hatim narrated from Ahmad ibn Sinan… Abu’l-Za’ra told us: ‘Abd-Allah said: Ruh al-Qudus (“the Holy Spirit”) is Jibril, then he said: something similar was narrated from Muhammad ibn Ka’b al-Qurazi, Qatadah, ‘Atiyyah al-‘Awfi, al-Saddi and al-Rabi’ ibn Anas.
Reference to the ‘Holy Spirit’ in the Sunnah
This view is supported by the above and by the report narrated by the two Shaykhs [al-Bukhari and Muslim] with their isnads from Abu Salamah ibn ‘Abd al-Rahman ibn ‘Awf, that he heard Hassan ibn Thabit al-Anaari asking Abu Hurayrah to bear witness, “I ask you by Allah, did you hear the Messenger of Allaah (peace and blessings of Allah be upon him) say, ‘O Hassan, respond on behalf of the Messenger of Allah. O Allah, support him with Ruh al-Qudus’?” Abu Hurayrah said, “Yes.” (Al-Tafsir al-Masbur by Dr. Hikmat Bashir, 1/192-193)
Shaykh al-Islam Ibn Taymiyah said: 
“The majority of scholars said that this refers to Jibril (peace be upon him), and that Allah called him al-Ruh al-Ameen, Ruh al-Qudus and Jibril.” (Daqaiq al-Tafsir, part 1, p. 310)
He wrote an entire chapter on that and said:
"Chapter on the meaning of Ruh al-Qudus:
Allah said (interpretation of the meaning):
“O ‘Isa (Jesus), son of Maryam (Mary)! Remember My Favour to you and to your mother when I supported you with Ruh ul Qudus [Jibril (Gabriel)]…” [al-Maidah 5:110]
Allah supported the Messiah (peace be upon him) with Ruh al-Qudus as He mentions in this ayah. In al-Baqarah Allah says (interpretation of the meaning):
“And We gave ‘Isa (Jesus), the son of Maryam (Mary), clear signs and supported him with Ruh-ul-Qudus [Jibril (Gabriel).] [al-Baqarah 2:87]
“Those Messengers! We preferred some of them to others; to some of them Allâh spoke (directly); others He raised to degrees (of honour); and to ‘Isa (Jesus), the son of Maryam (Mary), We gave clear proofs and evidences, and supported him with Ruh ul Qudus [Jibril (Gabriel)]” [al-Baqarah 2:253]
This is not limited only to the Messiah; others were also supported in this way. (The scholars) mentioned that Dawud said, “Do not stop supporting me with Ruh al-Qudus.” And our Prophet (peace and blessings of Allah be upon him) said to Hassan ibn Thabit, “O Allah, support him with Ruh al-Qudus.” According to another report: “Ruh al-Qudus will be with you so long as you are defending His Prophet.” Both versions are narrated in al-Sahih.
According to the Christians, the “Holy Spirit” dwelt in the Disciples, and according to them the “Holy Spirit” is something experienced by all of the Prophets. But Allah says in al-Nahl (interpretation of the meaning):
“Say (O Muhammad) Ruh ul Qudus [Jibril (Gabriel)] has brought it (the Quran) down from your Lord with truth, that it may make firm and strengthen (the faith of) those who believe, and as a guidance and glad tidings to those who have submitted (to Allah as Muslims).” [al-Nahl 16:102]
“Which the trustworthy Ruh [Jibril (Gabriel)] has brought down upon your heart (O Muhammad).” [al-Shu’ara’ 26:193]
“Whoever is an enemy to Jibril (Gabriel) (let him die in his fury), for indeed he has brought it (this Quran) down to your heart.” [al-Baqarah 2:97]
So it is clear that Ruh al-Qudus here refers to Jibril… No one suggests that Ruh al-Qudus means the life of Allah ; nor is this indicated by the wording and this phrase is never used in that sense.” (Daqaiq al-Tafsir, part 2, p. 92)
And Allah knows best.