  We present an analytical description of pi electrons of a finite size bilayer
graphene within a framework of the tight-binding model. The bilayered
structures considered here are characterized by a rectangular geometry and have
a finite size in one or both directions with armchair- and zigzag-shaped edges.
We provide an exact analytical description of the spectrum of pi electrons in
the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze
the dispersion relations, the density of states, and the conductance
quantization.
