  We present Herschel observations of the core of the Perseus cluster of
galaxies. The brightest cluster galaxy, NGC 1275, is surrounded by a network of
filaments previously imaged extensively in H{\alpha} and CO. In this work, we
report detections of FIR lines with Herschel. All but one of the lines are
spatially extended, with the [CII] line emission extending up to 25 kpc from
the core. There is spatial and kinematical correlation among [CII], H{\alpha}
and CO, which gives us confidence to model the different components of the gas
with a common heating model. With the help of FIR continuum Herschel
measurements, together with a suite of coeval radio, submm and infrared data,
we performed a SED fitting of NGC 1275 using a model that contains
contributions from dust emission as well as synchrotron AGN emission. The data
indicate a low dust emissivity index, beta ~ 1, a total dust mass close to 10^7
solar mass, a cold dust component with temperature 38 \pm 2 K and a warm dust
component with temperature of 116 \pm 9 K. The FIR-derived star formation rate
(SFR) is 24 \pm 1 solar mass per yr, in close agreement with the FUV-derived
SFR. We investigated in detail the source of the Herschel FIR and H{\alpha}
emissions emerging from a core region 4 kpc in radius. Based on simulations
conducted using the radiative transfer code, CLOUDY, a heating model comprising
old and young stellar populations is sufficient to explain these observations.
We have also detected [CII] in three well-studied regions of the filaments. We
find a [OI]/[CII] ratio about 1 dex smaller than predicted by the otherwise
functional Ferland (2009) model. The line ratio suggests that the lines are
optically thick, as is typical of galactic PDRs, and implies that there is a
large reservoir of cold atomic gas. [abridged]
