  All the principal results of this work concern the vertical transport in
generic three dimensional superlattices. In the 1st chapter we make an
historical introduction, then we discuss the geometry of the problem, and the
physical parameters associated with structure of electron minibands and
strength of external fields. We found the effect of collisionless transverse
magnetoresistance, and we discuss it in the 2nd chapter. This effect is similar
to collisionless Landau damping in a plasma and we utilize the same name. In
the 3rd chapter we provide quantum mechanical reasons for the above effect; we
show how a magnetic field bends narrow superlattice minibands, and we classify
the states into Landau-type and Stark-type. In the 4th chapter we compute
longitudinal magnetoresistance of superlattices due to the imperfections of the
interfaces. Correlation length of the interface roughness can be measured
independently by this method. In the 5th chapter we discuss the current-voltage
characteristic of superlattice when an electric field destroys the one-miniband
transport. We found that the structure of the high-field domains in the
superlattices is complicated, but can be described analytically with great
accuracy. This structure reveals itself in the details of the current-voltage
characteristics. All our results are consistent with existing experiments, and
we make careful comparison of theoretical predictions and experimental results
in all chapters.
