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Quark mixing, CP violation and rare decays after the top quark discovery

We review the highlights of quark mixing, particle-antiparticle mixing, CP violation and rare K- and B-decays in the Standard Model. The top quark discovery, the precise measurement of its mass, the improved knowledge of the couplings $V_{cb}$ and $V_{ub}$, and the calculations of NLO short distance QCD corrections improved considerably the predictions for various decay rates, the determination of the couplings $V_{td}$ and $V_{ts}$ and of the complex phase in the Cabibbo-Kobayashi-Maskawa matrix. After presenting the general theoretical framework for weak decays, we discuss the following topics in detail: i) the CKM matrix, its most convenient parametrizations and the unitarity triangle, ii) the CP-violating parameter $ε_K$ and $B^0_{d,s}-\bar B^0_{d,s}$ mixings, iii) the ratio $ε'/ε$, iv) the rare K-decays $K_L\toπ^0e^+e^-$, $K^+\toπ^+ν\barν$, $K_L\toπ^0ν\barν$ and $K_L\toμ^+μ^-$, v) the radiative decays $B\to X_sγ$ and $B\to X_s l^+l^-$, vi) the rare B-decays $B\to X_{s,d}ν\barν$ and $B_{d,s}\to l^+l^-$, vii) CP violation in neutral and charged B-decays putting emphasis on clean determinations of the angles of the unitarity triangle, and viii) the role of electroweak penguins in B-decays. We present several future visions demonstrating very clearly the great potential of CP asymmetries in B-decays and of clean K-decays such as $K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$ in the determination of the CKM parameters and in decisive testing of the Standard Model. An outlook for the coming years ends our review.