Geometry of Grand Unification

Grand Unification of all forces has been a well motivated paradigm for particle physics. This subject has been recently revisited in the context of string theory, leading to a geometric reformulation of the idea of unification of forces. The interplay between geometry and physics has led to a natural resolution to a number of puzzles of particle physics utilizing the geometry of extra dimensions of string theory. Here we review aspects of these developments for a mathematical audience (based on talks given in honor of Yau's 60th, Atiyah's 80th and Singer's 85th birthdays).