  We study here what it means for the Universe to be nearly flat, as opposed to
exactly flat. We give three definitions of nearly flat, based on density,
geometry and dynamics; all three definitions are equivalent and depend on a
single constant flatness parameter epsilon that quantifies the notion of nearly
flat. Observations can only place an upper limit on epsilon, and always allow
the possibility that the Universe is infinite with k=-1 or finite with k=1. We
use current observational data to obtain a numerical upper limit on the
flatness parameter and discuss its implications, in particular the
"naturalness" of the nearly flat Universe.
