  The twin group $T_n$ is a Coxeter group generated by $n-1$ involutions and
the pure twin group $PT_n$ is the kernel of the natural surjection of $T_n$
onto the symmetric group on $n$ letters. In this paper, we investigate
structural aspects of twin and pure twin groups. We prove that the twin group
$T_n$ decomposes into a free product with amalgamation for $n>4$. It is shown
that the pure twin group $PT_n$ is free for $n=3,4$, and not free for $n\ge 6$.
We determine a generating set for $PT_n$, and give an upper bound for its rank.
We also construct a natural faithful representation of $T_4$ into
$\operatorname{Aut}(F_7)$. In the end, we propose virtual and welded analogues
of these groups and some directions for future work.
