Inter-universal Teichmuller Theory I ------------------------------------ ・Corrected a slight defect in Fig. 4.1 ・Corrected a minor misprint concerning the reference to [IUTchII],  Remark 4.5.3, (i), in \S I1 ・Updated the Acknowledgements ・Slightly rephrased the definition of various tempered fundamental  groups in the discussion immediately following Remark 2.2.2 ・Corrected a misprint in the definition of \iota in the discussion  at the beginning of \S 1 ・Corrected a misprint "lattice lattice" in \S I4 ・Corrected a misprint at the beginning of the proof of Proposition 2.4 ・Corrected a minor misstatement in the proof of Lemma 2.7, (v) ・Added a supplementary reference to the displayed statement in Remark 3.1.2,  (ii) ・Corrected a minor inconsistency in the notation used in Example 3.2, (ii) ・Corrected a minor misprint in the notation involving "\otimes" in Example  3.5, (i) ・Added a supplementary reference to the discussion following Example 3.2,  (vi), (e) ・Corrected a minor misprint at the beginning of Proposition 6.5, (ii) ・Corrected a minor misprint at the end of Proposition 6.5, (iv) ・Slightly modified the discussion of poly-morphisms in \S 0 Inter-universal Teichmuller Theory II ------------------------------------- ・Corrected a slight error in the first display of Corollary 2.6, (i) ・Updated the Acknowledgements