We present results on searches for point-like sources of neutrinos using four years of IceCube data, including the first year of data from the completed 86-string detector. The total livetime of the combined dataset is 1,373 days. For an E$^{-2}$ spectrum the median sensitivity at 90% C.L. is $sim 10^{-12}$ TeV$^{-1}$cm$^{-2}$s$^{-1}$ for energies between 1 TeV$-$1 PeV in the northern sky and $sim 10^{-11}$ TeV$^{-1}$cm$^{-2}$s$^{-1}$ for energies between 100 TeV $-$ 100 PeV in the southern sky. The sensitivity has improved from both the additional year of data and the introduction of improved reconstructions compared to previous publications. In addition, we present the first results from an all-sky search for extended sources of neutrinos. We update results of searches for neutrino emission from stacked catalogs of sources, and test five new catalogs; two of Galactic supernova remnants and three of active galactic nuclei. In all cases, the data are compatible with the background-only hypothesis, and upper limits on the flux of muon neutrinos are reported for the sources considered.
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