  Clear power excess in a frequency range typical for solar-type oscillations
in red giants has been detected in more than 1000 stars, which have been
observed during the first 138 days of the science operation of the NASA Kepler
satellite. This sample includes stars in a wide mass and radius range with
spectral types G and K, extending in luminosity from the bottom of the giant
branch up to high-luminous red giants. The high-precision asteroseismic
observations with Kepler provide a perfect source for testing stellar structure
and evolutionary models, as well as investigating the stellar population in our
Galaxy. We fit a global model to the observed frequency spectra, which allows
us to accurately estimate the granulation background signal and the global
oscillation parameters, such as the frequency of maximum oscillation power. We
find regular patterns of radial and non-radial oscillation modes and use a new
technique to automatically identify the mode degree and the characteristic
frequency separations between consecutive modes of the same spherical degree.
In most cases, we can also measure the small separation. The seismic parameters
are used to estimate stellar masses and radii and to place the stars in an H-R
diagram by using an extensive grid of stellar models that covers a wide
parameter range. Using Bayesian techniques throughout our analysis allows us to
determine reliable uncertainties for all parameters. We provide accurate
seismic parameters and their uncertainties for a large sample of red giants and
determine their asteroseismic fundamental parameters. We investigate the
influence of the stars' metallicities on their positions in the H-R diagram. We
study the red-giant populations in the red clump and bump and compare them to a
synthetic population and find a mass and metallicity gradient in the red clump
and clear evidence of a secondary-clump population.
