Inter-universal Teichmuller Theory I ------------------------------------ ・In the portion of the second paragraph of \S 2 following the second display of the paragraph, slightly  modified the wording ("inclusions" ---> "[outer] inclusions") and added an explanatory phrase to the  final sentence of the paragraph Inter-universal Teichmuller Theory II ------------------------------------- ・Added a reference to Proposition 1.4 in the statement of Corollary 1.10 ・In Remark 1.10.1, added a reference to Corollary 1.10, reworded slightly inaccurate phrasing concerning projective  systems of mono-theta environments and deleted an unnecessary reference to [EtTh], Corollary 2.18, (ii) ・In Remark 1.10.3, added a reference to Remark 1.1.1 to the third sentence and some explanatory phrases to the final  sentence ・In Remark 1.11.3, (ii), slightly rephrased portions of the discussion surrounding the first display ・Slightly rephrased the final portion of Remark 1.11.3, (iii) ・Added a supplementary explanation to the final portion of Remark 1.11.3, (iv) ・In Remark 1.11.4, (ii), replaced "Now if" by "If" ・Added a supplementary explanatory reference to Example 1.8, (iv), towards the end of the statement of Corollary 1.2,  (iii) ・In the statement of Corollary 1.12, (c), slightly modified the reference to Example 1.8 ("(ii)" ---> "(ii), (iii)") ・Added a reference to Remark 1.11.4 at the end of Remark 1.12.2, (vi) ・Added a supplementary explanatory phrase "["roots" of]" in Remark 1.12.3 ・Slightly modified the phrasing of the second display of Remark 1.12.4 ("with forming" ---> "with the operation of  forming") ・Slightly rephrased the discussion of Remark 2.1.1, (ii), preceding the first display ・At the beginning of the statement of Proposition 2.2, added references to Remark 2.2.1; 1.4.1, (ii); 2.1.1, (ii) ・Corrected misprints ("1.6" ---> "1.6, (iii)", "\Pi" ---> "\Pi_{{\underline v}}") in the statement of Proposition 2.2, (ii) ・At the beginning of Definition 2.3, (i), added a reference to [IUTchI], Remark 3.1.1 ・Corrected a slight misstatement in the portion of Definition 2.3, (ii), that relates to [IUTchI], Corollary 2.5 ・Corrected slightly erroneous phrasing at the beginning of the second sentence of the statement of Corollary 2.4, (i) ・In Remark 2.4.1, replaced "the simplification" by "a simplification" ・Added references to Proposition 2.2, (i), and Corollary 2.4 to the final portion of the statement of Corollary 2.5, (i) ・Corrected a misprint ("the l-th" ---> "the reciprocals of the l-th") at the beginning of Remark 2.5.1, (ii) ・Deleted an unnecessary "=def" concerning the final tempered fundamental group listed in Remark 2.5.2, (ii) ・Slightly modified the wording of the first sentence of Corollary 2.6, (i), and the final sentence of Corollary 2.6, (ii);  made corresponding modifications to the final sentences of Corollary 2.8, (iii), and 2.9, (iii) ・Added references to Proposition 1.4 and Corollary 2.5, (i), in Definition 2.7, (ii) ・Added a reference to Corollary 2.5, (i), at the beginning of Corollary 2.9 ・In Proposition 3.1, (i), added a reference to Corollary 1.12, (d), and slightly modified the wording following the  second display ("above display" ---> "first display of the present (i)")