  We have used extensive V, I photometry (down to V=20.9) of 33615 stars in the
direction of the globular cluster M55 to study the dynamical interaction of
this cluster with the tidal fields of the Galaxy. An entire quadrant of the
cluster has been covered, out to ~2.0 times the tidal radius. A CMD down to
about 4 magnitudes below the turn-off is presented and analysed. A large
population of BS has been identified. The BS are significantly more
concentrated in the inner 300 arcsec, while they become less concentrated in
the cluster envelope. We have obtained luminosity functions at various radial
intervals from the center and their corresponding mass functions. Both clearly
show the presence of mass segregation inside the cluster. A dynamical analysis
shows that the observed mass segregation is compatible with what is predicted
by multi-mass King-Michie models. The global mass function is very flat with a
power-law slope of x=-1.0+/-0.4. This suggest that M55 might have suffered
selective losses of stars, caused by tidal interactions with the Galactic disk
and bulge. The radial density profile of M55 out to ~2.0 r_t suggests the
presence of extra-tidal stars whose nature could be connected with the cluster.
