  In this paper we show uniqueness of the conductivity for the quasilinear
Calder\'on's inverse problem. The nonlinear conductivity depends, in a
nonlinear fashion, of the potential itself and its gradient. Under some
structural assumptions on the direct problem, a real-valued conductivity
allowing a small analytic continuation to the complex plane induces a unique
Dirichlet-to-Neumann (DN) map. The method of proof considers some
complex-valued, linear test functions based on a point of the boundary of the
domain, and a linearization of the DN map placed at these particular set of
solutions.
