  In this paper we give an algorithm for counting the number of all independent
sets in a given graph which works in time $O^*(1.1394^n)$ for subcubic graphs
and in time $O^*(1.2369^n)$ for general graphs, where $n$ is the number of
vertices in the instance graph, and polynomial space. The result comes from
combining two well known methods "Divide and Conquer" and "Measure and
Conquer". We introduce this new concept of Divide, Measure and Conquer method
and expect it will find applications in other problems.
  The algorithm of Bj\"orklund, Husfeldt and Koivisto for graph colouring with
our algorithm used as a subroutine has complexity $O^*(2.2369^n)$ and is
currently the fastest graph colouring algorithm in polynomial space.
