Inter-universal Teichmuller Theory I
------------------------------------
・Added a supplementary phrase ("in the spirit of a 'topos' ") to the explanation
　of the notion of a Frobenioid in \S I1

・Corrected a misprint ("that in appear" ---> "that appear") in \S I1

・Slightly modified Figs. I1.5, 3.1

・Corrected misprints ("elements associated naturally associated" ---> "elements naturally 
　associated"), ("to note important role" ---> "to note the important role") in \S I2

・Corrected misprints ("constrast" ---> "contrast"), (de-italicized "of [AbsTopIII], \S 1)
　in \S I4

・Added a reference concerning "Uchida's Lemma" ([AbsTopIII], Proposition 1.3) to the discussion
　of \S I4

・Corrected a misprint in the definition of a "morphism of capsules of objects" in \S 0
　("A'_{j'}" ---> "A'_{\iota(j)}")

・Corrected a misprint in the discussion at the beginning of \S 1 ("Finally, we let us" --->
　"Finally, let us")

・Corrected a misprint in Definition 3.1, (e) ("finite etale" ---> "profinite etale")

・Updated the Acknowledgements

・Corrected misprints in Example 3.2, (v), (vi) ("of the category of the category" --->
　"of the category"), ("where ... are the monoids"), ("[SemiAnbd], Remark 3.4.1]" --->
　"[SemiAnbd], Remark 3.4.1].")

・Corrected a misprint in Remark 3.2.1, (ii) ("development of theory" ---> "development of
　the theory")

・Replaced the singular by the plural ("a certain minor oversight" ---> "certain minor oversights") 
　and added a supplementary explanation ("of residue characteristic p") to the beginning of Remark 
　3.2.4 

・Corrected a misprint in Remark 3.2.4, (iii) ("property (a) of (ii)" ---> ("property (a) of (i)")

・Added item (vi) to Remark 3.2.4

・Corrected a misprint in Remark 3.6.1 ("shall use apply" ---> "shall apply")

・Supplemented the explanation of the first display of Remark 3.8.1, (i)

・Corrected two misprints in Definition 4.1, (vi) ("be a collection" ---> "to be a collection")

・Corrected misprints in Remark 4.3.1, (ii) ("phenomonenon" ---> "phenomenon"), ("although the the" 
　---> "although the")

・Corrected a misprint in Remark 4.5.1, (iii) ("groups that that appear" ---> "groups that appear")

・Corrected misprints in Propositions 4.11, (i); 6.9, (i) ("elements of \in" ---> "elements of")

・Added a supplementary phrase to the discussion at the beginning of Remark 5.1.3 ("in F^\times_{mod}")

・Corrected a misprint in Remark 5.2.1, (ii) ("we shall we shall" ---> "we shall")

・Corrected a misprint in Proposition 6.7 ("relative via the" ---> "via the")

・Corrected a misprint in \S I2 ("for the the pairs" ---> "for the pairs")

Inter-universal Teichmuller Theory II
-------------------------------------
・Corrected a misprint in the Abstract ("another by means" ---> "another by means of")

・Updated the Acknowledgements

・Corrected a misprint at the beginning of Proposition 1.5 ("model mono-theta determined"
　---> "model mono-theta environment determined")

・Corrected a misprint in the discussion following the first display of Remark 1.5.2
　("image may is equal" ---> "image is equal")

・Corrected a misprint in Remark 1.11.3, (ii) ("possible take" ---> "possible to take")

・Corrected a misprint in the sentence preceding Corollary 1.12 ("discuss to main result"
　---> "discuss the main result")

・Slightly modified the second display of Corollary 1.12

・Corrected a misprint in Remark 3.6.2, (ii) ("allows one use" ---> "allows one to use")

・Corrected a misprint in Fig. 3.2 ("rigification" ---> "rigidification")

・Slightly modified the discussion of Remark 3.6.2, (iv)

・Corrected a misprint in Remark 3.6.4, (iii) ("ring str." ---> "ring structure")

・Corrected a misprint in Remark 4.7.4, (iii) ("to consist objects" ---> "to consist of objects")

・Slightly modified the fourth display of Definition 4.9, (i)

・Corrected a misprint in Remark 1.12.2, (i) ("lies in the the" ---> "lies in the")

・Added a supplementary phrase to the explanation following the final display of Proposition 1.4

・Added a supplementary explanation concerning the category "F" to the final portion of
　Corollary 1.10

Inter-universal Teichmuller Theory III
--------------------------------------
・Updated the Acknowledgements

・Corrected misprints in the Abstract and at the beginning of the Introduction
　("fact it allows" ---> "fact that it allows")

・Corrected a misprint in the discussion following Fig. I.2 ("prime-strips appear"
　---> "prime-strips that appear")

・Corrected a misprint in Remark 1.2.2, (iii) ("so as accommodate" ---> 
　"so as to accommodate")

・Corrected a misprint in Remark 1.3.3, (i) ("codomain the log-link" ---> 
　"codomain of the log-link")

・Corrected a misprint in Remark 1.5.1, (ii) ("is taken to a copy" ---> 
　"is taken to be a copy")

・Corrected a misprint in Remark 2.1.1, (i) ("equipped its natural" ---> 
　"equipped with its natural")

・Corrected a misprint in the sentence preceding Corollary 2.3 ("the present \S 3" --->
　"the present \S 2")

・Corrected a misprint in Remark 3.3.2, (ii) ("in the case of the case of" ---> 
　"in the case of")

・Corrected a misprint in Proposition 3.5, (ii), (c) ("contains of the entire torsion torsion" 
　---> "contains the entire torsion")

・Corrected a misprint in Remark 3.6.1 ("as far the" ---> "as far as the")

・Corrected a misprint in Remark 3.9.1, (ii) ("up a factor" ---> "up to a factor")

・Corrected three instances of a certain misprint in Theorem A, (i), (Ind1); 
　Remark 3.10.2, (ii); Theorem 3.11, (i), (Ind1) ("indetermacies" ---> "indeterminacies")

・Corrected a misprint in Remark 3.11.2, (ii) ("indentification" ---> "identification")

・Corrected a misprint in Remarks 2.2.2, (i); 3.11.2, (iv) ("the the" ---> "the")

・Corrected a misprint in Remark 3.11.3, (iv), (b) ("act on" ---> "act on the")

・Corrected a misprint in Step (vi) of the proof of Corollary 3.12 ("which have are" 
　---> "which are")

・Corrected misprints in Steps (x), (xi) of the proof of Corollary 3.12 ("with to 
　respect to" ---> "with respect to"), ("cf. the also the" ---> "cf. also the"),
　("object (0,0)" ---> "object at (0,0)")

・Added a supplementary phrase to the explanation preceding the second to last display
　of Step (xi) of the proof of Corollary 3.12

Inter-universal Teichmuller Theory IV
-------------------------------------
・Updated the Acknowledgements

・Corrected a misprint in Proposition 1.5, (i) ("up a factor" ---> "up to a factor")

・Corrected a misprint in the Introduction ("point of view the original" ---> "point of view
　of the original")

・Slightly modified the wording at the end of the statement of Proposition 1.1

・Corrected a misprint at the beginning of the proof of Proposition 1.3 ("exists an
　isomorphism R_0-algebras ---> "exists an isomorphism of R_0-algebras")

・Added an explanatory sentence to the proof of Proposition 1.3, (ii), concerning
　the positive real number \epsilon

・Corrected a misprint in the first sentence of the statement of Proposition 1.5

・Slightly modified the first sentence of the discussion preceding Proposition 1.8

・Slightly modified the beginning of the statement of Proposition 1.8, (i)

・Corrected a misprint at the beginning of the statement of Proposition 1.8, (ii)
　("G_k-module" ---> "module")

・Corrected a misprint in the proof of Proposition 1.8, (iv) ("Thus, a closed subgroup H^*"
　---> "Thus, the closed subgroup H^*")

・Added a supplementary phrase to the explanation preceding the final display of
　Theorem 1.10

・Corrected a slight inaccuracy in Step (ii) ("natural inclusion" ---> "natural outer
　inclusion")

・Corrected a misprint in Remark 1.10.2 ("may thought of as corresponding" ---> 
　"may be thought of as corresponding")

・Corrected a misprint in Remark 1.10.4, (b) ("ample line" ---> "ample line bundle") and
　slightly modified the wording of the precding sentence

・Corrected a misprint in Remark 1.10.5, (iii) ("left-hand side of inequality" --->
　"left-hand side of the inequality")

・Slightly modified the wording of the beginning of the statement of Corollary 2.2, (ii)

・Slightly modified the wording at the end of the third sentence of Remark 3.3.2