  The present paper is devoted to the classification of symplectic automorphisms of some hyperk\"{a}hler manifolds. The results contained here are an explicit classification of prime order automorphisms on manifolds of $K3^{[n]}$ type and a proof that all finite groups of symplectic automorphisms of such manifolds are contained in Conway's group $Co_1$. 
Towards a classification of symplectic automorphisms on manifolds of   $K3^{[n]}$ type