  Gromov's compactness theorem for pseudo-holomorphic curves is a foundational
result in symplectic geometry. It controls the compactness of the moduli space
of pseudo-holomorphic curves with bounded area in a symplectic manifold.
  In this paper, we prove the analog of Gromov's compactness theorem in
non-archimedean analytic geometry. We work in the framework of Berkovich
spaces.
  First, we introduce a notion of K\"ahler structure in non-archimedean
analytic geometry using metrizations of virtual line bundles. Second, we
introduce formal stacks and non-archimedean analytic stacks. Then we construct
the moduli stack of non-archimedean analytic stable maps using formal models,
Artin's representability criterion and the geometry of stable curves. Finally,
we reduce the non-archimedean problem to the known compactness results in
algebraic geometry. The motivation of this paper is to provide the foundations
for non-archimedean enumerative geometry.
