The Study of the Holy Spirit is called Pneumatology, it derives from the Greek word pneuma, meaning spirit, wind, or breath.
Christianity is the only religion with anything like a Holy Spirit.
The Holy Spirit is the Third Person of the Godhead, He is co-equal, co-eternal, co-existent with the Father and the Son, making Him just as beyond our understanding as the other members of the Godhead.
FYI: We have a simple answer for those questioning the doctrine of the Trinity. The Bible makes it quite clear that the Father is God, and that the Son is God, and that the Holy Spirit is God. It is also quite clear that there is only one God. You want a god you can understand we recommend Zeus. We are finite while His is infinite. There are just somethings that are beyond our ability to understand, the nature of God being one of them.
The Holy Spirit is given no name in Scripture. He has no name because the name we are to call upon is the Messiah’s. “Holy Spirit” is a title and is always a neuter noun. He is also called parakletos i.e. The Comforter/Helper/Counselor and that is a masculine noun in greek grammar.
16 And I will pray the Father, and he will give you another Counselor, to be with you for ever, 17 even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him; you know him, for he dwells with you, and will be in you. John 14:16-17
But the Counselor, the Holy Spirit, whom the Father will send in my name, he will teach you all things, and bring to your remembrance all that I have said to you. John 14:26
But when the Counselor comes, whom I shall send to you from the Father, even the Spirit of truth, who proceeds from the Father, he will bear witness to me; John 15:26
7 Nevertheless I tell you the truth: it is to your advantage that I go away, for if I do not go away, the Counselor will not come to you; but if I go, I will send him to you. 8 And when he comes, he will convince the world concerning sin and righteousness and judgment: John 16:7-8
13 When the Spirit of truth comes, he will guide you into all the truth; for he will not speak on his own authority, but whatever he hears he will speak, and he will declare to you the things that are to come. 14 He will glorify me, for he will take what is mine and declare it to you. 15 All that the Father has is mine; therefore I said that he will take what is mine and declare it to you. John 16:13-15
The Holy Spirit works to provide us with comfort or help while we are physically apart from Messiah. It is He who convinces the world of sin, and not our words.
. . . it is the Spirit himself bearing witness with our spirit that we are children of God, Rom. 8:16
Likewise the Spirit helps us in our weakness; for we do not know how to pray as we ought, but the Spirit himself intercedes for us with sighs too deep for words. Rom. 8:26