In the first part of the talk, a mathematical model and numerical
computation for the evolution of crystal surface in three-dimensions
by surface diffusion with anisotropic surface free energy is
presented. The model is governed by a fourth-order nonlinear
time-dependent partial differential equation. The method of lines is
used in the numerical computation. Employing this model we study the
entire evolution path of a single crystal to equilibrium. We examine
examples of simple cubic crystals with different levels of anisotropic
surface free energy and different initial crystal configurations.  In
the second part of the talk, a model and computation for the
coalescence of two particles is presented. We propose a proper set of
joining conditions and show the effect of surface diffusion on the
grain boundary motion. Finally, we compare simulation to a
experimental result.