Searching for New Physics in b → sℓ+ℓ− Transitions at the LHCb Experiment Introduction The LHCb Detector at the Large Hadron Collider Differential Branching Fraction of Λb0 → Λµ+µ− Angular Analysis of Λb0 → Λµ+µ− Decays Testing Lepton Favour Universality with RK∗0 Conclusions. This thesis presents two analyses of semileptonic b → sl+l− decays using Flavour Changing Neutral Currents (FCNCs) to test for the presence of new physics and lepton ﬂavour universality and the equality of couplings for different leptons which on the basis of experimental evidence is assumed to hold in the Standard Model free from uncertainties as a result of knowledge of the hadronic matrix elements. It also includes the angular analysis of Lambda_b >Lambda mumu decay and the RK* measurement both of which are first measurements not yet performed by any other experiment.