  We show that the graph of the classical Weierstrass function
$\sum_{n=0}^\infty \lambda^n \cos (2\pi b^n x)$ has Hausdorff dimension
$2+\log\lambda/\log b$, for every integer $b\ge 2$ and every $\lambda\in
(1/b,1)$. Replacing $\cos(2\pi x)$ by a general non-constant $C^2$ periodic
function, we obtain the same result under a further assumption that $\lambda b$
is close to $1$.
