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The field of spin electronics, or spintronics, is very broad and includes the investigation of spin dependent processes in a wide range of nanostructures. These lectures will be devoted to quantum theory of spintronic phenomena in magnetic tunnel junctions. The first part of lectures includes theory of tunnel magnetoresisitence (TMR) in single and double barrier magnetic tunnel junctions using free-electron and first-principle (ab-initio) approaches. In particular, it will be shown how ab-initio description of electronic structure properties led to prediction of a new phenomenon called Bloch states symmetry filtering effect which gives rise to a huge TMR values in crystalline magnetic tunnel junctions.