  We study the double Yangian associated with the Lie superalgebra
$\mathfrak{gl}_{m|n}$. Our main focus is on establishing the
Poincar\'{e}-Birkhoff-Witt Theorem for the double Yangian and constructing its
central elements in the form of coefficients of the quantum contraction. Next,
as an application, we introduce reflection algebras, certain left coideal
subalgebras of the level 0 double Yangian, and find their presentations by
generators and relations.
