Flyleaf
The flyleaf is the free half of the endsheet, which is a sheet (endsheet), folded in half to connect the cover and book block. It’s the loose part that isn’t glued down, sitting right before or after of the book block. Think of the very first sheet you lift when you open the cover of a hardcover book. Flyleaf refers to the sheet, both its front and reverse sides.
More on Endsheet, Pasteddown and Flyleaf
A red arrow pointing to the flyleaf, which is the right side of an endsheet