  We have studied solar-like oscillations in ~800 red-giant stars using Kepler
long-cadence photometry. The sample includes stars ranging in evolution from
the lower part of the red-giant branch to the Helium main sequence. We
investigate the relation between the large frequency separation (Delta nu) and
the frequency of maximum power (nu_max) and show that it is different for red
giants than for main-sequence stars, which is consistent with evolutionary
models and scaling relations. The distributions of nu_max and Delta nu are in
qualitative agreement with a simple stellar population model of the Kepler
field, including the first evidence for a secondary clump population
characterized by M ~> 2 M_sun and nu_max ~ 40-110 muHz. We measured the small
frequency separations delta nu_02 and delta nu_01 in over 400 stars and delta
nu_03 in over 40. We present C-D diagrams for l=1, 2 and 3 and show that the
frequency separation ratios delta nu_02/Delta nu and delta nu_01/Delta nu have
opposite trends as a function of Delta nu. The data show a narrowing of the l=1
ridge towards lower nu_max, in agreement with models predicting more efficient
mode trapping in stars with higher luminosity. We investigate the offset
epsilon in the asymptotic relation and find a clear correlation with Delta nu,
demonstrating that it is related to fundamental stellar parameters. Finally, we
present the first amplitude-nu_max relation for Kepler red giants. We observe a
lack of low-amplitude stars for nu_max ~> 110 muHz and find that, for a given
nu_max between 40-110 muHz, stars with lower Delta nu (and consequently higher
mass) tend to show lower amplitudes than stars with higher Delta nu.
