  We prove a global uniqueness result for the Calder\'{o}n inverse problem for
a general quasilinear isotropic conductivity equation on a bounded open set
with smooth boundary in dimension $n\ge 3$. Performing higher order
linearizations of the nonlinear Dirichlet--to--Neumann map, we reduce the
problem of the recovery of the differentials of the quasilinear conductivity,
which are symmetric tensors, to a completeness property for certain anisotropic
products of solutions to the linearized equation. The completeness property is
established using complex geometric optics solutions to the linearized
conductivity equation, whose amplitudes concentrate near suitable two
dimensional planes.
