  We present results of an optical search for Cepheid variable stars using the
Hubble Space Telescope (HST) in 19 hosts of Type Ia supernovae (SNe Ia) and the
maser-host galaxy NGC 4258, conducted as part of the SH0ES project (Supernovae
and H0 for the Equation of State of dark energy). The targets include 9 newly
imaged SN Ia hosts using a novel strategy based on a long-pass filter that
minimizes the number of HST orbits required to detect and accurately determine
Cepheid properties. We carried out a homogeneous reduction and analysis of all
observations, including new universal variability searches in all SN Ia hosts,
that yielded a total of 2200 variables with well-defined selection criteria --
the largest such sample identified outside the Local Group. These objects are
used in a companion paper to determine the local value of H0 with a total
uncertainty of 2.4%.
