  We study a class of planar continuous piecewise linear vector fields with
three zones. Using the Poincar\'e map and some techniques for proving the
existence of limit cycles for smooth differential systems, we prove that this
class admits at least two limit cycles that appear by perturbations of a period
annulus. Moreover, we describe the bifurcation of the limit cycles for this
class through two examples of two-parameter families of piecewise linear vector
fields with three zones.
