The papers of this prominent physicist document his scientific research, his life as an academic, his lifelong activities with Jewish affairs,and his personal life and travels. A sizeable portion of the collection concerns his research and academic affairs, including correspondence, manuscripts, lectures, notes, speeches, pamphlets, and audio tapes. A second major series documents Green's participation in Jewish affairs with organizations such as the Academic Committee on Soviet Jewry and the Allied Jewish Appeal of Philadelphia. Green's work to permit the emigration of Soviet scientists is documented in correspondence with the Union of Concerned Scientists.

The third major series documents Green's extensive travels to Israel, Japan, Europe, and Mexico, through extensive correspondence files. Prominent correspondents include Cyril Domb, co-author of a monographic series on Phase transition and critical phenomena, and A.V. Voronel, a Soviet scientist. This series includes correspondence, handbills, leaflets, photographs. The collection also includes minutes and telegrams. There are also materials associated with the 1973 Conference on renormalization theory.

The collection also documents Green's tenure as an instructor at Temple University, which includes lecture and research notes, as well as student files and correspondence.