Graphene, a single atomic sheet of graphite, is a monolayer of carbon atoms arranged in a hexagonal lattice. The unique electronic band structure of graphene exhibits an unusual low-energy linear dispersion relation, radically different from the parabolic bands common to all previous two-dimensional systems. Most interestingly, the charge carriers in graphene mimic relativistic, massless Dirac particles, leading to intriguing new phenomena. In this talk, I focus on two projects related to graphene that complement each other: magneto- transport measurements in high magnetic fields, and infrared optical studies of graphene. In the transport experiments, we discovered a room temperature quantum Hall effect in graphene  and new quantum Hall phases in the extreme quantum limit [2,3]. In the infrared experiments, we performed infrared transmission measurements in graphene [4,5], and resolved resonances between hole Landau levels and electron Landau levels (intraband transitions), as well as resonances between hole and electron Landau levels (interband transitions). For both projects, we argue that many-body correlations of massless Dirac Fermions contribute considerably to our experimental results.