The OT Shema (Deut. 6:4) and the NT indicate there is one God (Eph. 4:6, 1Tim. 2:5), and the NT teaches that the one God relates to believers in three ways simultaneously: as the Father, as the Son and as the HS. Whereas God the Father is mainly described as creator or initiator (Gen. 1:1) and God the Son mainly as Messiah or mediator (1Tim. 2:5), God the HS is mainly described as indweller of believers (Rom. 5:5, 1 John 4:7, Gal. 5:22, Eph. 2:18). These descriptions commonly use three prepositions: God the Father is over all creation (Eph. 4:6), God the Son is Immanuel or with humanity (Matt. 1:23), and the HS is within all believers (Eph. 1:13-19, cf. 1Cor. 8:6).
The HS is not frequently mentioned in the OT except in Isaiah (Isa. 4:4, 11:2, 42:1, 44:3, 48:16, 59:21, 61:1, 63:10), but He is more fully revealed in the NT. The HS is cited as somehow causing the virgin Mary to be pregnant with Jesus (via implanting a zygote untainted by sin?), although this fact was communicated to Joseph by an “angel of the Lord” (Matt. 1:18-23, Luke 1:26-35). The HS also filled the parents of John, Elizabeth and Zechariah (Luke 1:41&67), but an angel of the Lord told them that John would be filled with the HS from the womb (Luke 1:15). The HS then caused Simeon to prophesy that Jesus was Christ (Luke 2:25-35).
John the Baptist said that Jesus would baptize his followers with the HS, and the HS came upon Jesus after his baptism by John (Matt. 3:11-17, Luke 3:16-22), after which the HS filled Jesus and led him into the desert to be tempted by the devil (Matt. 4:1, Luke 4:1-2). Jesus described the HS as the Counselor and Teacher of Truth who would indwell his disciples following his death (John 14:16-17 & 25-26, 15:26, 16:13-15). The HS is mentioned frequently in the book of Acts (Acts 1:5, 2:4, 9:17, 13:2, 19:2), and in many of Paul’s letters (Rom. 8:4-26, 1Cor. 6:19, Eph. 4:30) as well as in some of the other epistles (2Pet. 1:21, Jude 20).