  The main purpose of this note is to prove an upper
  bound on the number of lattice points of a centrally symmetric
  convex body in terms of the successive minima of the body. This bound
  improves on former bounds and narrows the gap towards a lattice
  point analogue of Minkowski's second theorem on successive minima.
  Minkowski's proof of his second theorem is rather lengthy and it was
  also criticised as obscure. We present a short proof of Minkowski's
  second theorem on successive minima, which, however, is based on the
  ideas of Minkowski's proof.
