He earned a bachelor's degree with highest honors from the University of Illinois in 1955, where he was a member of Phi Beta Kappa.

Glitman later completed a master's degree in 1956, from the Tufts University, Fletcher School of Law and Diplomacy.

Glitman's early foreign postings included Nassau, Bahamas, Ottawa, Canada and Paris, France.

During the hiatus in the talks caused by the walk out of the Soviet delegation, he was posted to Vienna, Austria where he served as the Chief United States Representative, to the Mutual and Balanced Force Reduction Negotiations.

Those talks successfully concluded in 1987, when the U.S. Senate ratified the INF treaty eliminating an entire class of nuclear weapons, a significant achievement in the ending of the Cold War.