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%%% 11-15 October 1999, should be prepared.
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{\large\bf Theory of spin-dependent transport in nanostructures} \\

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{\underline{Patrick Bruno}}\\

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{\small{\em
Max-Planck-Institut f\"ur Mikrostrukturphysik, Weinberg 2, D-06120 Halle, 
Germany}} \\

{\tt bruno@mpi-halle.de}
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\noindent
The rapid expansion of the new field of spin-electronics sets
some new challenges to the theory. After a rapid discussion of the
important phenomena that have been investigated experimentally (giant
magnetoresistance, tunneling magneto-resistance, spin-polarized transport in 
semi-conductors, etc.), I shall present a
survey of the various methods that have been or could be proposed to 
tackle the
problem theoretically, and discuss their merits and weaknesses. Then I
shall discuss in more details an approach based upon the non-equilibrium
Green's function formalism (Kadanoff-Baym-Keldysh formalism) and present
projects based upon this method under development at the MPI in Halle.


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