  Young (125 Myr), populous ($>$1000 members), and relatively nearby, the
Pleiades has provided an anchor for stellar angular momentum models for both
younger and older stars. We used K2 to explore the distribution of rotation
periods in the Pleiades. With more than 500 new periods for Pleiades members,
we are vastly expanding the number of Pleiads with periods, particularly at the
low mass end. About 92\% of the members in our sample have at least one
measured spot-modulated rotation period. For the $\sim$8\% of the members
without periods, non-astrophysical effects often dominate (saturation, etc.),
such that periodic signals might have been detectable, all other things being
equal. We now have an unusually complete view of the rotation distribution in
the Pleiades. The relationship between $P$ and $(V-K_{\rm s})_0$ follows the
overall trends found in other Pleiades studies. There is a slowly rotating
sequence for $1.1\lesssim(V-K_{\rm s})_0\lesssim 3.7$, and a primarily rapidly
rotating population for $(V-K_{\rm s})_0\gtrsim 5.0$. There is a region in
which there seems to be a disorganized relationship between $P$ and $(V-K_{\rm
s})_0$ for $3.7 \lesssim(V-K_{\rm s})_0\lesssim 5.0$. Paper II continues the
discussion, focusing on multi-period structures, and Paper III speculates about
the origin and evolution of the period distribution in the Pleiades.
