The Maslov Index plays a central role in the geometric view (proof) of the Morse Index Theorem. The theorem is about geodesics which are curves and therefore dependent on a single (real) variable and the Maslov Index is a topological count of the conjugate points. The Maslov Index is extended to the case of elliptic PDEs in multi-dimensional domains and generalized Morse Index Theorems will be discussed. This is joint work with J. Deng, J.Marzuola and G.Cox.