A review is presented of the earliest stages of protostellar evolution
. Observations of pre-stellar cores, which are believed to represent t
he initial conditions for protostellar collapse, depart significantly
from the scale-free density distribution which is usually taken as the
starting point for the formation of a low-mass protostar. Pre-stellar
cores are observed to have radial density profiles which have hat inn
er regions, steepening towards their edges. This is seen to qualitativ
ely match the predictions of the Bonnor-Ebert stability criterion for
pressure-bounded self-gravitating gas clouds. From these initial condi
tions, theoretical modelling of cores threaded by magnetic fields pred
icts that quasi-static evolution by the process of ambipolar diffusion
will lead to a significantly different starting point for collapse th
an the static singular isothermal sphere. This departure from a scale-
free density distribution for the initial conditions has recently been
shown to produce an ensuing protostellar collapse which has a non-con
stant accretion rate. Recently published observations of low-mass prot
ostars in the rho Ophiuchi cluster are demonstrated to be consistent w
ith such a non-constant protostellar mass accretion rate, contrary to
the standard protostellar collapse model. Instead, the data appear con
sistent with an initially high accretion rate, which subsequently deca
ys. The initial phase of high accretion rate is labelled the 'main acc
retion phase', during which greater than or equal to 50 per cent of th
e circumstellar envelope mass is accreted in similar to 10 per cent of
the total accretion time, and which is equated observationally with C
lass 0 objects. The subsequent phase with roughly an order of magnitud
e lower accretion rate is labelled the 'late accretion phase', during
which the remainder of the envelope mass is accreted in the remaining
similar to 90 per cent of the total accretion time, at an order of mag
nitude lower accretion rate, and which is equated observationally with
Class I objects. The growth of circumstellar discs begins in the Clas
s 0 stage, and proceeds through the Class I and II stages. Published d
ata of the Taurus star-forming region currently available appear also
to be consistent with this scenario.