of Asaph = by Asaph. The fifth of the twelve Asaph Psalms. App-63. Psa_76:1, Psa_76:5, Psa_76:8, and Psa_76:11 are in the third person. Psa_76:4, Psa_76:7, Psa_76:10 and are in the second person. The Structure is determined by the two Selahs; and points to the historic event, the taking of Jebus by David (2Sa_5:4-9) 960B.C.
Judah. Great emphasis on the locality. Note the three terms, Judah, Salem, Zion, and "there" (Psa_76:3).
God. Hebrew. Elohim.App-4.
known = made known, or making Himself known.
Israel. Named because the taking of Jebus was in connection with David's taking of the throne of Israel.