In this thesis we present a unified model for dense core formation and collapse within

post-shock dense layers inside giant molecular clouds. Supersonic converging flows

collide to compress low density gas to high density clumps, inside which gravitational

collapse can happen. We consider both spherically symmetric and planar converging flows,

and run models with inflow Mach number from 1.1-9 to investigate

the relation between core properties and the bulk velocity dispersion of the mother cloud.

Four stages of protostar formation are identified: core building, core collapse,

envelope infall, and late accretion. The core building stage takes 10 times as long as core

collapse, which lasts a few 105 yr, consistent with observed

prestellar core lifetimes. We find that the density profiles of cores during collapse can

be fitted by Bonnor-Ebert sphere profiles, and that the density and velocity profiles

approach the Larson-Penston solution at the core

collapse instant. Core shapes change from oblate to prolate as they evolve. Cores with

masses varying by three orders of magnitude ~ 0.05 - 50 solar mass are identified in

our high Mach number simulations, and a much smaller mass range for models having low

Mach number. The median core mass versus Mach number lies between the minimum mass

that can collapse in late times Ma-1 and the most evolved core

mass Ma-1/2. We implement sink particles to the grid code Athena

to track the collapse of other dense regions of a large scale simulation after the most

evolved core collapses, We demonstrate use of our code for applications with a

simulation of planar converging supersonic turbulent flows, in which multiple cores form

and collapse to create sinks; these sinks continue to interact and accrete from their

surroundings over several Myr.