I saw that one definition of Euclidean metric is
There exists a coordinate $x^1,\ldots,x^n$, $x^i=x^i(z)$ such that $\det(\frac{\partial x}{\partial z})\neq 0$ and $g_{ij} = \frac{\partial x^k}{\partial z^i}\frac{\partial x^k}{\partial z^j}$ (sum over repeated index).
Then the book said that then the metric with respect to the coordinate $x$ is $g'_{ij} = \delta_{ij}$ by a change of coordinates. I wonder if you could explicitly explain how is the change of coordinate done?