The presence of the Holy Spirit among God’s people is to be a source of unity. Christians are to maintain the “unity of the Spirit” (Eph. 4:3). The HS binds God’s people together in a bond of peace.
Every Christian has access to God through the same Spirit (Eph. 2:19), another evidence that all are equal in Christ, that the body of Christ is a place of peace and unity, because Christ is our peace (2:14). Barriers, divisions, and enmities are destroyed in Christ, and the Holy Spirit is part of that process. God dwells in the church, the peaceful body of Christ, so the church is described as the dwelling place of God through the Spirit (2:20).
The Holy Spirit dwells in each Christian individually (see previous lessons, also 1 Cor. 6:19-20). The Holy Spirit also dwells in Christians corporately, that is in the body or the church (1 Cor. 3:16).
In John 17, the Father and the Son are one (a unity) because they share the same thinking, goals, and glory. The unity of believers depends on their receiving the word (17:14), which is truth (17:17). That word empowered the testimony of the early believers so that even more came to believe (17:20). There is no explicit mention of the Holy Spirit in John 17, but the principle is clear.
The unity of the Father, Son and Spirit is the model for the unity of the church today.