  We consider the classification of fractal square dendrites $K$ based on the
types of the self-similar boundary $\partial K$ and the main tree $\gamma$ of
such dendrites. We show that the self-similar boundary of a fractal square
dendrite $K$ may be of 5 possible types and may consist of 3,4 or 6 points.
  We prove that the main trees of fractal square dendrites belong to 7 possible
classes. Bearing in mind the placement and orders of the points of $\partial K$
with respect to the main tree $\gamma$, this results in 16 possible types of
main trees for non-degenerate fractal square dendrites.
