Neutralino dark matter, and in particular different aspects of its detection at neutrino telescopes, has been studied within the Minimal Supersymmetric extension of the Standard Model, the MSSM. The relic density of neutralinos has been calculated using sophisticated routines for integrating the annihilation cross section and the Boltzmann equation. As a new element, so called coannihilation processes between the lightest neutralino and the heavier neutralinos and charginos have also been included for any neutralino mass and composition. The detection rates at neutrino telescopes have been evaluated for neutralino annihilation in both the Sun and the Earth using detailed Monte Carlo simulations of the whole chain of processes from the neutralino annihilation products in the core of the Sun or the Earth to detectable muons at a neutrino telescope. A comparison with other searches for supersymmetry at accelerators and direct dark matter searches is also given. The signal muon fluxes that current and future neutrino telescopes can probe and the improvement in sensitivity that can be achieved with angular and/or energy resolution of the neutrino-induced muons has also been investigated. The question of whether the neutralino mass can be extracted from the width of the muon angular distribution, if a signal flux is observed, has also been addressed.
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