  We give an exposition of the theory of invariant manifolds around a fixed
point, in the case of time-discrete, analytic dynamical systems over a complete
ultrametric field K.
  Typically, we consider an analytic manifold M modelled on an ultrametric
Banach space over K, an analytic self-map f of M, and a fixed point p of f.
Under suitable conditions on the tangent map of f at p, we construct a
centre-stable manifold, a centre manifold, respectively, an r-stable manifold
around p, for a given positive real number r not exceeding 1.
  The invariant manifolds are useful in the theory of Lie groups over local
fields, where they allow results to be extended to the case of positive
characteristic which previously were only available in characteristic zero
(i.e., for p-adic Lie groups).
