Successive Minima and Lattice Points
  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. 
Martin Henk