I'll give a gentle introduction to the beautiful theory of hyperkahler manifolds. These extremely symmetric manifolds are important for many applications to mathematics and physics, and I'll introduce many examples and known constructions. As time permits, I'll discuss recent work indicating how to construct, explicitly, the first nontrivial compact hyperkahler manifold -- the so-called K3 manifold. (처음 1시간은 미분다양체론을 수강한 모든 대학원생들을 위한 pretalk 이며 다음 1시간은 research talk 입니다.)