Hyperk¨ahler manifolds have appeared at first within the framework of differential geometry as an example of Riemannian manifolds with holonomy of a special restricted type. However, they have soon exhibited such diverse and unexpected links with various branches of mathematics that now hyperk¨ahler geometry by itself forms a separate research subject. Among the traditional areas fused within this new subject are differential and algebraic geometry of complex manifolds, holomorphic symplectic geometry, geometric representation theory, Hodge theory and many others. The most recent addition to the list is the link between hyperk¨ahler geometry and theoretical physics: it turns out that hyperk¨ahler manifolds play a critical part in the modern version of the string theory, which is in itself the basis for the future unified field theory and quantum gravity.