  The pseudo-Riemannian manifold $M=(M^{4n},g), n \geq 2$ is para-quaternionic
K\" ahler if $hol(M) \subset sp(n, \RR) \oplus sp(1, \RR).$ If $hol(M) \subset
sp(n, \RR),$ than the manifold $M$ is called para-hyperK\" ahler. The other
possible definitions of these manifolds use certain parallel para-quaternionic
structures in $\End (TM),$ similarly to the quaternionic case. In order to
relate these different definitions we study para-quaternionic algebras in
details. We describe the reduction method for the para-quaternionic K\" ahler
and para-hyperK\" ahler manifolds and give some examples. The decomposition of
a curvature tensor of the para-quaternionic type is also described.
