  A new measurement of elastic $pp$ scattering at $\sqrt{s} = 13$ TeV with the
ATLAS-ALFA detector is presented. The measurement was performed using data
recorded in a special run of the LHC with $\beta^\star = 2.5$ km. The elastic
cross-section was measured differentially in the Mandelstam $t$ variable and
from a fit to ${\textrm{d}}\sigma/\textrm{d}t$ the total cross section, the
$\rho$-parameter and parameters of the nuclear slope are determined. The
results for $\sigma_{\textrm{tot}}$ and $\rho$ are \begin{equation*}
\sigma_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \; \pm 1.1 \; \mbox{mb} ,
  \; \; \rho = \mbox{0.098} \; \pm 0.011 . \end{equation*} The energy evolution
of $\sigma_{\textrm{tot}}$ and $\rho$, connected through dispersion relations,
is compared to several models. Furthermore, the total inelastic cross section
is determined from the difference of the total and elastic cross section, and
the ratio of the elastic to total cross section is calculated.
