Inter-universal Teichmuller Theory I ------------------------------------ ・Slightly modified the discussion surrounding the second display of Example 4.3, (i) ・Corrected a misprint in Remark 4.9.1, (ii) ("necessary the" ---> "necessary to") ・Corrected a misprint in Example 5.4, (iv) ("post-compostion" ---> "post-composition") ・Slightly modified certain of the notational conventions ("\circledcirc" ---> "\circledast", "{\underline v}" ---> "v")  introduced in Example 5.1 and Definition 5.2 (cf., especially, the notation that is equipped with a subscript "mod" or  a subscript "\kappa") Inter-universal Teichmuller Theory II ------------------------------------- ・Slightly modified certain of the notational conventions ("\circledcirc" ---> "\circledast", "{\underline v}" ---> "v")  so as to conform to the newly modified versions of the notational conventions introduced in [IUTchI], Example 5.1, and  [IUTchI], Definition 5.2 (cf., especially, the notation that is equipped with a subscript "mod" or a subscript "\kappa") Inter-universal Teichmuller Theory III -------------------------------------- ・Slightly modified certain of the notational conventions ("\circledcirc" ---> "\circledast", "{\underline v}" ---> "v")  so as to conform to the newly modified versions of the notational conventions introduced in [IUTchI], Example 5.1, and  [IUTchI], Definition 5.2 (cf., especially, the notation that is equipped with a subscript "mod" or a subscript "\kappa") Inter-universal Teichmuller Theory IV ------------------------------------- ・Updated the Acknowledgements ・Corrected a misprint ("field k," ---> "field,") in the first sentence of Proposition 1.8 ・Added the label "(P7)" to a certain property that appears in a display in the proof of Corollary 2.2  and slightly modified the discussion surrounding this property (P7) ・Added item (vii) to Remark 2.3.1