[en] Recently the radiative B-decay to strange axial-vector mesons, B → K₁(1270)γ, was observed with a rather large branching ratio. This process is particularly interesting as the subsequent K₁-decay into its three-body final state allows us to determine the polarization of the photon, which is mostly left(right)-handed for B-bar(B) in the Standard Model while various new physics models predict additional right(left)-handed components. In this thesis, a new method is proposed to determine the polarization, exploiting the full Dalitz plot distribution, which seems to reduce significantly the statistical errors on the polarization parameter λ_γ measurement. This polarization measurement requires, however a detailed knowledge of the K₁ → Kππ strong interaction decays, namely, the complex pattern of various partial wave amplitudes into the several possible quasi-two-body channels as well as their relative phases. A number of experiments have been done to extract all these information while there remain various problems in the previous studies. In this thesis, we investigate the details of these problems. As a theoretical tool, we use the ³P₀ quark-pair-creation model in order to improve our understanding of strong K₁-decays. Finally we try to estimate some theoretical uncertainties: in particular, the one coming from the uncertainty on the K₁ mixing angle, and the effect of a possible 'off-set' phase in strong decay S-waves. According to our estimations, the systematic errors are found to be of the order of σ_λγ(th) ≤ 20%. On the other hand, we discuss the sensitivity of the future experiments, namely the SuperB factories and LHCb, to λ_γ. Naively estimating the annual signal yields, we found the statistical error of the new method to be σ_λγ(stat) ≤ 10% which turns out to be reduced by a factor 2 with respect to using the simple angular distribution. We also discuss a comparison to the other methods of the polarization measurement using processes, such as B → K^*e⁺e^-, B_d → K^*γ and B_s → φγ, for the determination of the ratio of the Wilson coefficients C_7γ^eff'/C_7γ^eff. We show an example of potential constraints on the Wilson coefficients ratio in several scenarios of supersymmetric models. (author)