Selected problems around Higgs bosons

In these lectures I consider selected problems related to the Higgs bosons. Firstly, in a very simplified treatment I derive thee upper and lower limits for the mass of the standard Higgs argueing that it should be between ∼250 GeV and ∼1 TeV. If the mass of the Higgs boson is larger than 1 TeV, the ''strong-weak'' interaction is inevitable which could lead particularly to the Regge trajectories for gauge bosons, quarks and leptons with the slope of order of approx1 TeV. The main part of the lectures is devoted to the theory of the pseudo-Goldstone boson-axion and another, purely, Goldstone boson - ''massless axion'', or ''arion''. The mass of the axion and its couplings to nucleon are obtained by using the method of diagnolizing the mass matrix of pseudo Goldstone degrees of freedom relevant to the problem. In analizing the properties of the arion we exploit the resemblance of the arion exchange of the usual magnetic interaction. At the end of the lectures some possible and actually performed experiments for the search of arions are described. (orig.)