This book focuses on current topics in quasicrystal science and research. Various themes are addressed, such as atomic structure, growth of quasicrystals, statistical physics and thermodynamics, magnetism, phasons, propagation of waves, surfaces and technological potential of quasicrystals. Insight into basics in physics and chemistry is also given, with examples from metallurgy, the surface of alloys, plasticity, etc., in order to point out the possible genuine aspects of quasicrystals and allow a better comparison with conventional alloys.