The concept of a “Spirit” that permeates the cosmos is a feature of most religions (e.g. Brahman in Hinduism and Tao in Taoism and Great Spirit among Indigenous peoples of the Americas), however the term Holy Spirit specifically refers to the beliefs held in the Abrahamic religions.
For the majority of Christians, the Holy Spirit is the third person of the Holy Trinity: Father, Son, and Holy Spirit, and is Almighty God. The Holy Spirit is seen as one Person of the Triune God, who revealed His Holy Name YHWH to his people Israel, sent His Eternally Begotten Son Jesus to save them from God’s wrath, and sent the Holy Spirit to sanctify and give life to his Church. The Triune God manifests as three Persons, in One Divine Being , called the Godhead, the Divine Essence of God.
In Judaism, there are many references to The Spirit of God, Ruach HaKodesh, The Holy Spirit of YHWH, however it has rejected any idea of The Eternal God as being either Dual or Triune. The term ruach ha-kodesh (Hebrew: רוח הקודש, “holy spirit” also transliterated ruah ha-qodesh) occurs once in Psalm 51:11 and also twice in the Book of Isaiah. Those are the only three times that the precise phrase “ruach hakodesh” is used in the Hebrew Scriptures, although the noun ruach (רוח, literally “breath” or “wind”) in various combinations, some referring to God’s “spirit”, is used often. The noun ruach, much like the English word breath, can mean either wind or some invisible moving force.
However, the word Shekinah is derived from the Hebrew verb שכן, meaning literally to settle, inhabit, or dwell, which suggests the concept of a Holy Spirit, and is used frequently in the Hebrew Bible.
In Islam, the Holy Spirit (Arabic: الروح القدس al-Ruh al-Qudus, “the-Spirit the-Holy”) is mentioned several times in the Qur’an, where it acts as an agent of divine action or communication. In Hadith it is commonly identified with the angel Gabriel (Arabic Jibreel). The Spirit (الروح al-Ruh, without the adjective “holy”) is also used as the creative spirit from God by which God enlivened Adam, and inspired the angels and the prophets. The belief in Trinity, as it is defined in the Qur’an, is explicitly forbidden by the Qur’an and called a grave sin.
The Bahá’í Faith has the concept of the Most Great Spirit, seen as the bounty of God. It is used to describe the descent of the Spirit of God upon the messengers/prophets of God, known as Manifestations of God, and include among others Jesus, Muhammad and Bahá’u'lláh. The Bahá’í believe the Holy Spirit is a conduit through which the wisdom of God becomes directly associated with his messenger, and it has been described variously in different religions such as the burning bush to Moses, the sacred fire to Zoroaster, the dove to Jesus, the angel Gabriel to Muhammad, and the maid of heaven to Bahá’u'lláh. The Bahá’í reject the idea that the Holy Spirit is a partner to God in the Godhead, but rather is the pure essence of God’s attributes.
(Names of God – Holy Spirit)