This is Volume 1 of a two-volume set which contains 18 invited papers in honour of the 80th birthday of mathematician Israel M. Gelfand, who is considered to have played an important role in the development of functional analysis in the latter half of the 20th century. The papers cover areas in which Gelfand has a strong interest, including geometric quantum field theory, representation theory, combinatorial structures underlying various "continuous" constructions, quantum groups and geometry.
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