Measurements of CP violation and the CKM matrix at LHCb

Precise measurements of the CKM unitarity triangle angles are key goals of the LHCb physics programme. This paper presents the steps foreseen for the measurement of the CP-violating phase related to the $B_s^0 \to J/\psi\phi$ decay. This observable is predicted to be very small in the Standard Model, while many models of New Physics lead to significant enhancements. LHCb has the capability to improve significantly the existing experimental knowledge on this phase with the data expected in the 2010 run, and to probe down to the Standard Model prediction within a few years of operation. A short review is also given of other CP measurements sensitive to New Physics