Edwin Henry Spanier (August 8, 1921, Washington, D.C.–October 11, 1996, Scottsdale, Arizona) was an American mathematician at the University of California at Berkeley, working in algebraic topology. He co-invented Spanier–Whitehead duality and Alexander–Spanier cohomology, and wrote what was for a long time the standard textbook on algebraic topology (Spanier 1981).
Spanier attended the University of Minnesota, graduating in 1941. During World War II, he did his service in the United States Army Signal Corps. He received his Ph.D. from the University of Michigan in 1947; his thesis, written under the direction of Norman Steenrod, was entitled Cohomology Theory for General Spaces. After spending a year as a research fellow at the Institute for Advanced Study in Princeton, New Jersey, he was appointed to the faculty of the University of Chicago in 1948, and then professor at Berkeley in 1959.