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The present work is mostly focused on theoretical §study of multiferroics and magnetic semiconductors §within the framework of density functional theory §(DFT). Being based on a dissertation, this book is §mainly addressed to graduated students working in §the area. However, the results and techniques §presented, can be of interest for any scientist in §the field of material sciences. One of the §multiferroics studied here is Bi2NiMnO6. This was §recently synthesized as a heavily distorted double §perovskite. The calculated results for magnetization §and ferroelectricity are also shown. A second study §shows the results of completely relaxed electronic §structure calculations for multiferroic §LaMnO3/BaTiO3 structure which was built by joining a §slab of magnetic LaMnO3 with a slab of ferroelectric §BaTiO3. The study of Mn doped GeTe, which is a §diluted magnetic semiconductor (DMS), shows the net §magnetization as a function of doping and holes §concentration. In addition, it is presented a study §of ferroelectric GeTe and the properties §exhibited by Si(001)/Si(110) junction which was §experimentally built using hybrid orientation §technology (HOT).