  The determination of the absolute scale of the neutrino masses is one of the
most challenging present questions in particle physics. The most stringent
limit, $m(\bar{\nu}_{\mathrm{e}})<2$eV, was achieved for the electron
anti-neutrino mass \cite{numass}. Different approaches are followed to achieve
a sensitivity on neutrino masses in the sub-eV range. Among them, experiments
exploring the beta decay or electron capture of suitable nuclides can provide
information on the electron neutrino mass value. We present the Electron
Capture $^{163}$Ho experiment ECHo, which aims to investigate the electron
neutrino mass in the sub-eV range by means of the analysis of the
calorimetrically measured energy spectrum following electron capture of
$^{163}$Ho. A high precision and high statistics spectrum will be measured with
arrays of metallic magnetic calorimeters. We discuss some of the essential
aspects of ECHo to reach the proposed sensitivity: detector optimization and
performance, multiplexed readout, $^{163}$Ho source production and
purification, as well as a precise theoretical and experimental
parameterization of the calorimetric EC spectrum including in particular the
value of $Q_{\mathrm{EC}}$. We present preliminary results obtained with a
first prototype of single channel detectors as well as a first 64-pixel chip
with integrated micro-wave SQUID multiplexer, which will already allow to
investigate $m(\nu_{\mathrm{e}})$ in the eV range.
