Lattice-QCD predicts the existence of a new form of hot, dense matter called the Quark Gluon Plasma (QCP) above a critical energy density. Such matter is believed to be created in relativistic heavy-ion collisions, where sufficient energy is expected to be deposited by colliding ions in a limited volume. To study the properties of the QCP, high transverse momentum (p_T) partons produced at the early stage of the collisions are used as probes. Since partons are not directly measurable, jet reconstruction, which assembles the hadron fragments of a parton into a "jet", provides an experimental tool to reconstruct the parton kinematics. When traversing the colored medium, partons lose energy via both induced gluon radiation and elastic scatterings. Consequently jet structure is modified relative to jets generated in vacuum. The inclusive differential jet cross section in pp collisions at [special characters omitted] = 2.76 TeV is measured, which serves as a reference for jet measurements in Pb-Pb collisions at the same [special characters omitted]. Two jet cone radii are used to reconstruct jets, and the ratio of the cross sections is formed. The good agreement between these results and perturbative QCD calculations at Next-to-Leading Order confirms the validity of the theoretical calculations in a new energy regime. Performing the same analysis in Pb-Pb collisions is challenging because of the large background. Therefore, a novel approach using the difference of the jet distributions recoiling from trigger hadrons in two disjoint p_T intervals is developed to remove the contribution of background jets. In this thesis, azimuthal correlations between trigger hadrons and recoil jets are studied; and seen to remain essentially the same in pp and Pb-Pb collisions, implying that jets are not further deflected in the medium. These results are consistent with radiating multiple relatively soft (low p _T) gluons instead of a single hard (high p_T) one as the preferred way for partons to lose energy in the medium.