TITLE: Eigenvalues of Laplacian
QUESTION [6 upvotes]: What's the most natural way to establish the asymptotics of $\Delta$  on a compact Riemannian manifold $M$ of dimension $N$? The asymptotics should be 
$$ \#\{v < A^2\} = \mathrm{const}\ast\mathrm{vol}(M)\ast A^n + o(\mathrm{something}) $$
(Perhaps one could consider first the case of a Kähler manifold? The Laplacian is particularly simple there.)

REPLY [2 votes]: Wener Müler - Weyl laws...
http://www.math.uni-bonn.de/people/mueller/papers/weyllaw.pdf 
has a pretty good introduction. 
Edit: I see now that only the second section addresses you specific question and not the intro:(