In this section, generalizations of the instanton theory and the modified WKB theory described in Chapter 2 to multidimensional space are presented [43]. Those who are not interested in the generalization of the instanton approach and the proof of its equivalence to the modified WKB theory can skip Section 6.1.1 and Section 6.1.2. In Section 6.1.3 a general WKB formulation for a general Hamiltonian in curved space is provided and its final expression of tunneling splitting can be directly applied to any real systems.