"The notion of infinitely near s is classical and well understood for s. We generalize the notion to higher dimensions and to develop a general theory, in terms of idealistic exponents and certain s associated with them. We then gain a refined generalization of the classical notion of first characteristic exponents. On the level of technical base in the higher dimensional theory, there are some powerful tools, referred to as Three Key Theorems, which are namely Differentiation Theorem, Numerical Exponent Theorem and Ambient Reduction Theorem."