  We describe several methods of constructing R-matrices that are dependent
upon many parameters, for example unitary R-matrices and R-matrices whose
entries are functions. As an application, we construct examples of R-matrices
with prescribed singular values.
  We characterise some classes of indecomposable set-theoretic solutions of the
quantum Yang-Baxter equation (QYBE) and construct R-matrices related to such
solutions. In particular, we establish a correspondence between one-generator
braces and indecomposable, non-degenerate involutive set-theoretic solutions of
the QYBE, showing that such solutions are abundant.
  We show that R-matrices related to involutive, non-degenerate solutions of
the QYBE have special form.
  We also investigate some linear algebra questions related to R-matrices.
