[7] Baum received his early education at the parochial school of St. Peter's Parish in Kansas City, and began to serve as an altar boy at the church at age ten.

[8] He entered St. John's Minor Seminary in 1940, and then studied philosophy in the undergraduate program at Cardinal Glennon College in Shrewsbury, Missouri.

[6] The diocese then sent him to study in Rome at the Pontifical University of St. Thomas Aquinas, where he earned a Doctor of Sacred Theology degree in 1958.

[6] Returning to Kansas City, Baum resumed his teaching duties at St. Theresa College (1958–63) and served as secretary of the Diocesan Tribunal.

[5] From 1962 to 1965, Baum served as a peritus, or theological expert, in Rome for Bishop Charles Helmsing at the Second Vatican Council.

[8] In that capacity, he worked with the Secretariat for Christian Unity and helped draft Unitatis Redintegratio, the council's decree on ecumenism.

[7] In 1964, he was named the first executive director of the Committee on Ecumenical and Interreligious Affairs for the National Conference of Catholic Bishops, a post which he held for five years.

[1] He received his episcopal consecration on April 6, 1970, from Cardinal John Carberry, with Bishops Charles Helmsing and Joseph Sullivan serving as co-consecrators.

His resignation as Penitentiary was accepted the day after his 75th birthday in 2001, but he remained active in Rome to the extent that his health permitted, and attended the meeting of American cardinals called to deal with the sex abuse scandal in 2003.