  The stability method is very useful for obtaining exact solutions of many
extremal graph problems. Its key step is to establish the stability property
which, roughly speaking, states that any two almost optimal graphs of the same
order $n$ can be made isomorphic by changing o(n^2) edges.
  Here we show how the recently developed theory of graph limits can be used to
give an analytic approach to stability. As an application, we present a new
proof of the Erdos-Simonovits Stability Theorem.
  Also, we investigate various properties of the edit distance. In particular,
we show that the combinatorial and fractional versions are within a constant
factor from each other, thus answering a question of Goldreich, Krivelevich,
Newman, and Rozenberg.
