Special values of multiple polylogarithms

Historically, the polylogarithm has attracted specialists and nonspecialist s alike with its lovely evaluations. Much the same can be said for Euler su ms (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we ha ve been forced to consider multidimensional extensions encompassing the cla ssical polylogarithm, Euler sums, and the Riemann zeta function. Here, we p rovide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove sev eral previously conjectured evaluations, including an intriguing conjecture of Don Zagier.