If $d(x,y)$ and $e(x,y)$ are metrics then $d(x,y)+e(x,y)$ and $\frac{d(x,y)}{1+d(x,y)}$ are metrics.

If $d\_i(x,y)$ for $i=1,\dots,n$ are metrics then so is $\sqrt{\sum\_{i=1}^n{d\_i^2(x,y)}}$

Are there other interesting ways of constructing new metrics from old metrics?