  This thesis is devoted to studying strong coupling phenomena (and confinement
in particular) in supersymmetric gauge theories. The central object of
investigation is the non-Abelian string that is responsible for the
"instead-of-confinement" phase for monopoles in 4D ${\mathcal N} = 2$
supersymmetric QCD with the U($N$) gauge group and $N_f$ flavors of quark
hypermultiplets, $N \leqslant N_f \leqslant 2 N$.
  Here it is shown that the non-Abelian strings and confined monopoles survive
when we transition to the ${\mathcal N} = 1$ supersymmetric QCD. To this end we
consider a mass term $\mu$ for the adjoint matter, and in the limit of large
$\mu$ the bulk theory flows to ${\mathcal N} = 1$. We consider this transition
both from the bulk point of view and from the world sheet theory, which is the
two-dimensional $\mathbb{CP}(N-1)$ model. Survival of monopoles in the
${\mathcal N} = 1$ supersymmetric QCD is important for the
"instead-of-confinement" phase, and also for the Seiberg-Witten picture of
confinement.
  Apart from that, we also consider non-Abelian vortex strings in 4D
$\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$
flavors of quark hypermultiplets. It has been recently shown that these
vortices behave as critical superstrings. In particular, the lowest string
state appears to be a massless BPS "baryon." Here we show the occurrence of
this stringy baryon using a purely field-theoretic method. Moreover, we
explicitly demonstrate the "instead-of-confinement" phase, when the screened
quarks and gauge bosons of weak coupling are replaced by the confined
monopole-antimonopole pairs of strong coupling.
  English version. Full text (Russian and English) is available at the official
web page https://go.spbu.ru/20a2711 .
