The cubic-kilometer sized IceCube neutrino observatory, constructed in the glacial ice at the South Pole, searches indirectly for dark matter via neutrinos from dark matter self-annihilations. It has a high discovery potential through striking signatures. This thesis presents searches for dark matter annihilations in the center of the Sun using experimental data collected with IceCube.

The main physics analysis described here was performed for dark matter in the form of weakly interacting massive particles (WIMPs) with the 79-string configuration of the IceCube neutrino telescope. For the first time, the DeepCore sub-array was included in the analysis, lowering the energy threshold and extending the search to the austral summer. Data from 317 days live-time are consistent with the expected background from atmospheric muons and neutrinos. Upper limits were set on the dark matter annihilation rate, with conversions to limits on the WIMP-proton scattering cross section, which initiates the WIMP capture process in the Sun.These are the most stringent spin-dependent WIMP-proton cross-sections limits to date above 35 GeV for most WIMP models.

In addition, a formalism for quickly and directly comparing event-level IceCube data with arbitrary annihilation spectra in detailed model scans, considering not only total event counts but also event directions and energy estimators, is presented. Two analyses were made that show an application of this formalism to both model exclusion and parameter estimation in models of supersymmetry.

An analysis was also conducted that extended for the first time indirect dark matter searches with neutrinos using IceCube data, to an alternative dark matter candidate, Kaluza-Klein particles, arising from theories with extra space-time dimensions.

The methods developed for the solar dark matter search were applied to look for neutrino emission during a flare of the Crab Nebula in 2010.