Abstract: We give an introduction to the Standard Model of particle physics, as it is derived in the mathematical framework of noncommutative geometry. Using not much more mathematics but matrix
multiplication, the emergent picture of the fine structure of spacetime is that of the product of the continuum with a noncommutative finite space. The latter describes the internal degrees of freedom, which
are now translated in terms of geometry.
In the second part of the talk, we will discuss some of the physical consequences of our approach. We argue that there is a natural candidate to go Beyond the Standard Model, involving a Pati-Salam gauge
symmetry at higher energy. We justify our approach by analyzing the running of the Pati-Salam gauge couplings, with boundary conditions set by the (usual) Standard Model couplings at an intermediate mass
scale at which the Pati-Salam symmetry is broken. We find that the three Pati-Salam gauge couplings meet in a single point and hence establish grand unification.