The Morse and Maslov indices for matrix Hill's equations

To Fritz Gesztesy on the occasion of his 60-th birthday with best wishes Abstract. For Hill's equations with matrix valued periodic potential, we dis- cuss relations between the Morse index, counting the number of unstable eigen- values, and the Maslov index, counting the number of signed intersections of a path in the space of Lagrangian planes with a xed plane. We adapt to the