  We perform a detailed classification of the Lie point symmetries and of the
resulting similarity transformations for the Generalized Boiti-Leon-Pempinelli
equations. The latter equations for a system of two nonlinear 1+2 partial
differential equations of second- and third-order. The nonlinear equations
depend of two parameters, namely $n$ and $m$, from where we find that for
various values of these two parameters the resulting systems admit different
number of Lie point symmetries. For every case, we present the complete
analysis for the admitted Lie group as also we determine all the possible
similarity solutions which follow from the one-dimensional optimal system.
Finally, we summarize the results by presenting them in a tabular way.
