  We describe an interesting interplay between symbolic dynamics, the structure
of the Mandelbrot set, permutations of periodic points achieved by analytic
continuation, and Galois groups of certain polynomials.
  Internal addresses are a convenient and efficient way of describing the
combinatorial structure of the Mandelbrot set, and of giving geometric meaning
to the ubiquitous kneading sequences in human-readable form (Sections 3 and 4).
A simple extension, \emph{angled internal addresses}, distinguishes
combinatorial classes of the Mandelbrot set and in particular distinguishes
hyperbolic components in a concise and dynamically meaningful way.
  This combinatorial description of the Mandelbrot set makes it possible to
derive existence theorems for certain kneading sequences and internal addresses
in the Mandelbrot set (Section~6) and to give an explicit description of the
associated parameters. These in turn help to establish some algebraic results
about permutations of periodic points and to determine Galois groups of certain
polynomials (Section~7).
  Through internal addresses, various areas of mathematics are thus related in
this manuscript, including symbolic dynamics and permutations, combinatorics of
the Mandelbrot set, and Galois groups.
