  Bose-Einstein condensation and the $\lambda$-transition are described in
molecular detail for bosons interacting with a pair potential. New phenomena
are identified that are absent in the usual ideal gas treatment. Monte Carlo
simulations of Lennard-Jones helium-4 neglecting ground momentum state bosons
give a diverging heat capacity approaching the transition. Pure permutation
loops give continuous growth in the occupancy of the ground momentum state.
Mixed ground and excited momentum state permutation loops give a discontinuous
transition to the condensed phase. The consequent latent heat for the
$\lambda$-transition is 3\% of the total energy. The predicted critical
velocity for superfluid flow is within a factor of three of the measured values
over three orders of magnitude in pore diameter.
