Many astronomical observations, including rotational curve measurements of stars and the analysis of the cosmic microwave background, suggest the existence of an invisible matter density content in the Universe, commonly called Dark Matter (DM). Possibly, DM could be of particle nature, where Weakly Interacting Massive Particles (WIMPs) could be a viable DM candidate. The cubic-kilometer sized IceCube neutrino observatory located at the Earth’s South Pole can search indirectly for the existence of DM by detecting neutrino signals from WIMP self-annihilation in the Galactic center (GC) and the Galactic halo (GH). Two main physics analyses were developed and conducted to search indirectly for WIMP self-annihilation in the Milky Way’s GC and GH. Signal hypotheses for different WIMP annihilation channels, WIMP masses and DM halo profiles were tested. The results of both analyses were compatible with the background-only hypothesis for all tested signal hypotheses. Thus, upper limits at the 90% confidence level (C.L.) on the thermally averaged DM self-annihilation cross-section, &lt;σΑv&gt;, were set. Dedicated atmospheric muon veto techniques have been developed for the GC search making such an IceCube analysis possible for the first time. The GC analysis utilized data from 319.7 days of live-time of the IceCube detector running in its 79-string configuration during 2010 and 2011, whereas the GH analysis utilized pre-existing data samples developed for point-like neutrino sources with a live-time of 1701.9 days between 2008 and 2013. The most stringent upper limits on &lt;σΑv&gt; were obtained for WIMP annihilation directly into a pair of neutrinos assuming a Navarro-Frenk-White (NFW) DM halo profile. Conducting the GC and GH analyses for this annihilation channel an upper limit on &lt;σΑv&gt; as low as 4.0 · 10-24 cm3 s-1 and 4.5 · 10-24 cm3 s-1 is set for a 65 GeV and 500 GeV massive WIMP, respectively. These galactic indirect neutrino searches for DM are complementary to the indirect gamma-ray DM searches usually performed on extra-galactic targets like spheroidal dwarf galaxies. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 2: Manuscript.</p>