Quasicrystals are metallic alloys that exhibit atomic scale order, but not periodic order. Atomic scale properties of these materials are different from single crystalline material, for example, extraordinary mechanical properties, electrical and thermal transport properties, and electronic structure. This book presents topical research in the study of quasicrystals, including vacancies in quasicrystals; the formation of quasicrystals in bulk metallic glasses and their effects on mechanical behaviour; the electrical transport observed in Al-Pd-Mn quasicrystals; logarithmic periodicity in quasicrystals; and positron annihilation studies of quasicrystals.