  In this paper we analyze the classical XXZ spin chain with reflecting
boundaries. We exhibit a system of log-canonical coordinates on the phase space
generalizing Sklyanin's separation of variables for the periodic XXZ chain, and
use these coordinates to construct action-angle variables for the system. We
also integrate the flows of the reflection Hamiltonians explicitly in terms of
Riemann theta functions. Central to our analysis is the algebraic integrability
of the model.
