The goal of this work is to treat the main boundary value problems for the Stokes system, i.e.,

(i) the Dirichlet problem with L^p -data and nontangential maximal function estimates,

(ii) the Neumann problem with L^p -data and nontangential maximal function estimates,

(iii) the Regularity problem with L(...) -data and nontangential maximal function estimates,

(iv) the transmission problem with L^p -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.