There Is One Spirit
While God is a Spirit, and both Father and Son are "God," they both are "Spirit" (John 4:24; 1:1f). Still, there is only one "Holy Spirit." The Spirit's work is Paul's object when he wrote: "There is one Spirit."
Jesus revealed the Spirit's work in varying statements he made to the Apostles the night of His sad betrayal by Judas. The Apostles were promised the "Comforter who will be with you forever" (John 14:16). The Holy Spirit would teach the apostles all things and remind them of things Jesus had taught them while he was yet with them (John 14:26). The Holy Spirit would "bear witness" of Christ (John 15:26). The Comforter would guide apostles into "all truth" and declare unto them "all things to come" (John 16:13). He would glorify the Son (John 16:14). The Spirit would convict the world "in respect of sin, and of righteousness and of judgment" (John 16:8). From these passages Jesus reveals that there are some things the Spirit would do for the apostles, for Him and for the world.
The apostles were promised the Spirit's comfort and guidance. These messengers of Christ would meet trying, perplexing and fearful things when they fulfilled the commission Jesus had given them. The constant presence of the Holy Spirit would be of immense comfort to them, reassuring was the knowledge they need not worry what to say when they stood before magistrates and kings. "But when they deliver you up, be not anxious how or what ye shall speak: for it shall be given you in that hour what ye shall speak. For it is not you that speak, but the Spirit of your Father that speaketh in you" (Matthew 10:19f). He would remind them of Jesus' teaching which yet He was with them and reveal to them additional things He had not told them of. Moreover, with the Spirit's guidance, the apostles would speak things the Spirit revealed to them, "not in words which man's wisdom teacheth, but which the Spirit teacheth, combining spiritual things with spiritual words" (1 Corinthians 2:13). This passage is declaration of apostolic inspiration (which he mentions elsewhere, 2 Timothy 3:15-17) and which claim Peter also made (2 Peter 1:20f). We may have explicit trust in the New Testament for the Holy Spirit has given inerrantly us the word and will of Jesus.
The Spirit would glorify Christ (John 16:14). How so? He would glorify the Son by and through the revelations of the Son's Person and work. He is God (John 1:1f; Philippians 3:5f; Hebrews 1:3). The Holy Spirit would witness of Christ through the things He revealed the Son to be.
The Spirit would convict the world in respect of sin, righteousness and judgment. The world would be convicted as sinners for it had rejected Christ's testimony of Himself, which the Holy Spirit would establish. The world would be convicted of righteousness. That He was righteous and innocent was demonstrated when God raised Him from the dead and elevated Him to His right hand. He would convict the world of sin in that the prince of the world (Satan) has been judged. Christ destroyed Satan's power over man when he was victoriously raised from the dead (Hebrews 2:14f).
The Spirit works even today as His word is proclaimed and by it sinners are convicted of their sins and cry out "Brethren, what shall we do?" Do not resist the Holy Spirit as the people did in Stephen's day (Acts 7:51). "Today, if ye will hear his voice, harden not your hearts."