  Dirac points lie at the heart of many fascinating phenomena in condensed
matter physics, from massless electrons in graphene to the emergence of
conducting edge states in topological insulators [1, 2]. At a Dirac point, two
energy bands intersect linearly and the particles behave as relativistic Dirac
fermions. In solids, the rigid structure of the material sets the mass and
velocity of the particles, as well as their interactions. A different, highly
flexible approach is to create model systems using fermionic atoms trapped in
the periodic potential of interfering laser beams, a method which so far has
only been applied to explore simple lattice structures [3, 4]. Here we report
on the creation of Dirac points with adjustable properties in a tunable
honeycomb optical lattice. Using momentum-resolved interband transitions, we
observe a minimum band gap inside the Brillouin zone at the position of the
Dirac points. We exploit the unique tunability of our lattice potential to
adjust the effective mass of the Dirac fermions by breaking inversion symmetry.
Moreover, changing the lattice anisotropy allows us to move the position of the
Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a
critical limit, the two Dirac points merge and annihilate each other - a
situation which has recently attracted considerable theoretical interest [5-9],
but seems extremely challenging to observe in solids [10]. We map out this
topological transition in lattice parameter space and find excellent agreement
with ab initio calculations. Our results not only pave the way to model
materials where the topology of the band structure plays a crucial role, but
also provide an avenue to explore many-body phases resulting from the interplay
of complex lattice geometries with interactions [11, 12].
