  We present a catalogue of dense cores and filaments in a
$3.8^{\circ}\times2.4^{\circ}$ field around the TMC1 region of the Taurus
Molecular Cloud. The catalogue was created using photometric data from the
Herschel SPIRE and PACS instruments in the 70 $\mu$m, 160 $\mu$m, 250 $\mu$m,
350 $\mu$m, and 500 $\mu$m continuum bands. Extended structure in the region
was reconstructed from a Herschel column density map. Power spectra and PDFs of
this structure are presented. The PDF splits into log-normal and power-law
forms, with the high-density power-law component associated primarily with the
central part of TMC1. The total mass in the mapped region is 2000 M$_\odot$, of
which 34% is above an extinction of AV $\sim$ 3 mag -- a level that appears as
a break in the PDF and as the minimum column density at which dense cores are
found. A total of 35 dense filaments were extracted from the column density
map. These have a characteristic FWHM width of 0.07 pc, but the TMC1 filament
itself has a mean FWHM of $\sim$ 0.13 pc. The thermally supercritical filaments
in the region are aligned orthogonal to the prevailing magnetic field
direction. Derived properties for the supercritical TMC1 filament support the
scenario of it being relatively young. A catalogue of 44 robust and candidate
prestellar cores is created and is assessed to be complete down to 0.1
M$_\odot$. The combined prestellar CMF for the TMC1 and L1495 regions is well
fit by a single log-normal distribution and is comparable to the standard IMF.
