Abstract: In this talk, I will describe a general method of counting the number of ends for certain classes of complete, noncompact, Riemannian manifolds. A typical category of manifolds being considered are those whose bottom of the spectrum has maximal value relative to the lower bound of the Ricci curvature. Another class are locally symmetric spaces whose bottom of the spectrum is of maximal value relative to that of its universal covering. Finally, I will also give some results on manifolds of finite volume.