Tests of Lepton Flavour Universality and searches for Lepton Flavour Violation at LHCb

An embedded feature of the Standard Model is that different charged leptons have the same interaction strengths with the electroweak-force carriers. This is known as Lepton Flavour Universality (LFU). The LFU is an accidental symmetry of the SM, not the result of some fundamental underlying principle. Recent results on LFU tests in semileptonic $b\rightarrow c \ell \nu$ transitions and rare $b \rightarrow s \ell\ell$ decays, point to a violation of the LFU. If confirmed by further measurements, this would be clear evidence of New Physics in which new heavy particles couple preferentially to $2^{nd}$ or $3^{rd}$ generations of leptons. Many extensions of the SM that include violation of the LFU, predict Lepton Flavour Violating (LFV) processes in hadron decays with charged leptons in the final state. In this talk, the recent results from LHCb on LFU tests along with searches of charged-LFV are reported.