The Veni Creator Spiritus appears in manuscripts of the ninth and tenth centuries and entered the office of Pentecost, where it has remained. Medieval and later tradition ascribed it to Rabanus Maurus, the encyclopedic abbot of Fulda and archbishop of Mainz, an ascription first firmly attached centuries after his death and still argued over, with Charlemagne's court and other Carolingian authors proposed as alternatives, so the honest statement is that the hymn is Carolingian and its author unproven. Its theology is exact.
The Spirit is addressed as creator, not merely comforter, then under the titles the tradition gave, Paraclete, gift of God most high, living fountain, fire, charity and spiritual anointing. The hymn asks for the sevenfold gift, for light in the senses and love poured into hearts, for the enemy driven far off and peace given, and for knowledge of the Father and the Son, closing in a doxology to the Trinity. It is thus a compact pneumatology, the church's teaching on the Holy Spirit in seven singable quatrains, and its long metre made it endlessly translatable, into German by Luther, into English most famously in John Cosin's version, Come, Holy Ghost, our souls inspire, printed in the Book of Common Prayer's ordination rites.