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In 1982, a novel phase known as quasicrystal possessing a long-range orientational but quasiperiodic translational order was discovered in a rapidly solidified Al Mn alloy (Shechtman et al. Phys. Rev. Lett. 53 (1984: year of publication)). Quasicrystals are orientationally-ordered structures with classically forbidden rotation symmetries (e.g. fivefold and tenfold rotation axes) which are incompatible with the periodic translational ordering and this discovery has completely changed the understanding of crystallography. For this discovery, the 2011 Nobel Prize for Chemistry has been awarded to Professor Danny Shectman. Prof. Shechtman himself is said to have cried "Eyn chaya kazo", which translates from the Hebrew as "there can be no such creature". Over the last 25 years, quasicrystals have become the subject of intense experimental and theoretical studies. The present book is divided into seven chapters including introductory literature survey, review of classification, synthesis, structures, stability, properties and applications of quasicrystalline materials.