Joint work with Grzegorz Plebanek.

We present several results providing lower bounds and upper bounds for the Banach--Mazur distance
\[
{ \rm d_{BM}}\big( C(K), C(L)\big)
\]
between Banach spaces of continuous functions on compact spaces.
We begin with the case where $C(L)$ represents the classical Banach space $c$ of convergent sequences.
Some of the estimates in this part required computer-assisted calculations.
We follow with results for nonscattered spaces $K$ and $L$, focusing on the classical Banach spaces $L_\infty[0,1]$ and $\ell_\infty$, but also proving more general results.