  For a lattice polytope P, define A_P(t) as the sum of the solid angles of all
the integer points in the dilate tP. Ehrhart and Macdonald proved that A_P(t)
is a polynomial in the positive integer variable t. We study the numerator
polynomial of the solid-angle series sum_{t >= 0} A_P(t) z^t. In particular, we
examine nonnegativity of its coefficients, monotonicity and unimodality
questions, and study extremal behavior of the sum of solid angles at vertices
of simplices. Some of our results extend to more general valuations.
