In these lectures I first cover radiative and semileptonic B decays, including the QCD corrections for the quark subprocesses. The exclusive modes and the evaluation of the hadronic matrix elements, i.e. the relevant hadronic form factors, are the second step. Small effects due to the long-distance, spectator contributions, etc. are discussed next. The second section we start with non-leptonic decays, typically B \to \pi\pi ,  K\pi , \rho \pi,  \global \let \T1\textellipsis . . . We describe in more detail our predictions for decays dominated by the b \to s \eta _c transition. Reports on the most recent experimental results are given at the end of each subsection. In the second part of the lectures I discuss decays forbidden by the Lorentz and gauge invariance, and due to the violation of the angular momentum conservation, generally called the Standard Model-forbidden decays. However, the non-commutative QED and/or non-commutative Standard Model (NCSM), developed in a series of works in the last few years allow some of those decay modes. These are, in the gauge sector, Z \to \gamma \gamma, gg, and in the hadronic sector, flavour changing decays of the type K \to \pi \gamma , B \to K \gamma, etc. We shall see, for example, that the flavour changing decay D⁺_S\to \pi ⁺ \gamma dominates over other modes, because the processes occur via charged currents,  i.e. on the quark level they arise from the point-like photon x current x current interactions. In the last section we present the transition rate of ``transverse plasmon'' decay into a neutrino--antineutrino pair via non-commutative QED,  i.e. \gamma _pl\to \nu \bar \nu. Such decays give extra contribution to the mechanism for the energy loss in stars.

PACS numbers: 13.40.Hq, 13.20.He, 13.25.Hw, 12.60.Cn