Who Is He?
ho.ly

: exhalted or worthy of complete devotion as one perfect in goodness and righteousness.

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spirit noun (INNER CHARACTER)

the inner character of a person, thought of as different from the material person we can see and touch.

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A better question to ask is not "What", but "Who" is the Holy Spirit! He is a PERSON, the third person who makes up the TRIUNE being of God (The Father, The Son and The Holy Spirit). Similar to how water can take on the form of liquid, ice and vapour, so too God exists in different forms. 

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Jesus said, "But the Comforter (Counselor, Helper, Intercessor, Advocate, Strengthener, Standby), the Holy Spirit, Whom the Father will send in My name [in My place, to represent Me and act on My behalf], He will teach you all things. And He will cause you to recall (will remind you of, bring to your remembrance) everything I have told you." 
John 14:26 AMPC

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Who IS Holy Spirit?
The Holy Spirit came to reside within Jesus during his mission on earth. The Holy Spirit enabled The Son to access the thoughts, will, heart and power of The Father to fulfill the purpose of which He was sent for. It was by the POWER of the Holy Spirit that Jesus was able to resist all temptation and live a life free of sin. Jesus said in John 16:7 that it is to our advantage that He go away so that the Holy Spirit may come and give us FULL ACCESS to The Father. 

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Jesus is the gift to the unsaved.
The Holy Spirit is the gift to the saved.

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We are made in the image of God, and therefore are triune beings also. We are a SPIRIT that possesses a SOUL that lives in a BODY. The spirit is the very core being of a person. It is the life within that exists beyond the natural realm. Our bodies (or flesh) are of this world and are sinful by nature. The soul of man is the mediator between spirit and body. When we accept Jesus as our Lord and Saviour we receive HIS Holy Spirit-- the old spirit (once led by the desires of the flesh) dies and His spirit takes it’s place; this is referred to as being “BORN AGAIN”. The spirit, or “inner man”, is the part of us that becomes connected to God through union with the Holy Spirit and is the source by which we receive the power and anointing (God given ability) to walk in His good and perfect will. The Christian must now learn to live a life led by The Spirit and not our flesh.

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"For he who sows to his own flesh (lower nature, sensuality) will from the flesh reap decay and ruin and destruction, but he who sows to the Spirit will from the Spirit reap eternal life."
Galatians 6:8 AMPC

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"But you shall receive power (ability, efficiency, and might) when the Holy Spirit has come upon you, and you shall be My witnesses in Jerusalem and all Judea and Samaria and to the ends (the very bounds) of the earth." 
Acts 1:8 AMPC

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The Holy Spirit empowers us to walk in love and present ourselves as "living sacrifices" that guide people towards redemption in Jesus Christ. He is our number one HELPER along this great LOVE QUEST!