  Let $K$ be a compact Lie group. We introduce the process of symplectic
implosion, which associates to every Hamiltonian $K$-manifold a stratified
space called the imploded cross-section. It bears a resemblance to symplectic
reduction, but instead of quotienting by the entire group, it cuts the
symmetries down to a maximal torus of $K$. We examine the nature of the
singularities and describe in detail the imploded cross-section of the
cotangent bundle of $K$, which turns out to be identical to an affine variety
studied by Gelfand, Vinberg, Popov, and others. Finally we show that
``quantization commutes with implosion''.
