  We exploit the deepest existing far-infrared (FIR) data obtained so far by
Herschel at 100 and 160 um in the GOODS-N, as part of the PACS Evolutionary
Probe (PEP) survey, to derive for the first time the evolution of the
rest-frame 60-um, 90-um, and total IR luminosity functions (LFs) of galaxies
and AGNs from z=0 to unprecedented high redshifts (z~2-3). The PEP LFs were
computed using the 1/Vmax method. The FIR sources were classified by means of a
detailed broad- band SED-fitting analysis and spectral characterisation. Based
on the best-fit model results, k-correction and total IR (8-1000 um) luminosity
were obtained for each source. LFs (monochromatic and total) were then derived
for various IR populations separately in different redshift bins and compared
to backward evolution model predictions. We detect strong evolution in the LF
to at least z~2. Objects with SEDs similar to local spiral galaxies are the
major contributors to the star formation density (SFD) at z< 0.3, then, as
redshift increases, moderate SF galaxies - most likely containing a
low-luminosity AGN - start dominating up to z ~= 1.5. At >1.5 the SFD is
dominated by the contributions of starburst galaxies. In agreement with
previous findings, the comoving IR LD derived from our data evolves
approximately as (1 + z)^(3.8+/-0.3) up to z~1, there being some evidence of
flattening up to z~2.
