The goal of this work is to treat the main boundary value problems for the Stokes system, i.e.,
(i) the Dirichlet problem with Lp-data and nontangential maximal function estimates,
(ii) the Neumann problem with Lp-data and nontangential maximal function estimates,
(iii) the Regularity problem with L(...)-data and nontangential maximal function estimates,
(iv) the transmission problem with Lp-data and nontangential maximal function estimates,
(v) the Poisson problem with Dirichlet condition in Besov-Triebel-Lizorkin spaces,
(vi) the Poisson problem with Neumann condition in Besov-Triebel-Lizorkin spaces,
in Lipschitz domains of arbitrary topology in (...)n, for each n (...) 2. Our approach relies on boundary integral methods and yields constructive solutions to the aforementioned problems.