\magnification=1440 \font\bigtenrm=cmr10 scaled\magstep4 Abstract for Donald E. Knuth, Overlapping Pfaffians A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians. \bye .