Inter-universal Teichmuller Theory I ------------------------------------ ・Added an explanation of the notation "E_K" in the third paragraph of \S I1 ・Added an explanatory phrase ("[which we regard as equipped with the once-punctured elliptic  curve X_F]") in the fifth paragraph of \S I1 ・Corrected a misprint ("prototype for the the theory" ---> "prototype for the theory")  in \S I1 ・Added Remarks 1.2.2, 1.2.3; added references to Remark 1.2.2, (ii), to the various  references to [AbsTopI], Lemma 4.5, throughout the paper (8 instances) ・Slightly modified the wording at the beginning of Definition 3.1, (c) ("such that the  outer homomorphism" ---> "such that the image of the outer homomorphism") ・Slightly modified the wording of Definition 3.1, (e) ("taking an l-th root" ---> "extracting  an l-th root") ・Slightly modified the wording in the first sentence of Example 6.2, (i); Example 6.3, (i)  ("relative to the evident" ---> "relative to the tautological") ・Corrected misprints ("consitutent" ---> "constituent") in Definition 6.4, (i);  Definition 6.11, (i) Inter-universal Teichmuller Theory II ------------------------------------- ・Added a reference to [IUTchI], Remark 1.2.2, (ii), in Definition 2.3, (ii) ・Corrected a misprint ("inifnite" ---> "infinite") in Remark 2.6.3, (iii) ・Corrected a misprint ("of of" ---> "of") in the first sentence of Example 3.2 ・Corrected a misprint ("Put in another words" ---> "Put in other words") in Remark 3.5.2, (ii) Inter-universal Teichmuller Theory III -------------------------------------- ・Corrected a misprint ("On other hand" ---> "On the other hand") in Remark 1.5.4, (iii) ・Corrected 4 instances of a missing underline beneath a (math Fraktur) "log(...)" in  the second display of Proposition 3.4, (i), and the explanation immediately following  this display; the first display of Proposition 3.7, (ii); the reference to Proposition  3.7, (ii), in Remark 3.10.1, (i) Inter-universal Teichmuller Theory IV ------------------------------------- ・Corrected a misprint ("On other hand" ---> "On the other hand") in the proof of Proposition 1.1 ・Slightly modified the references to [BogIUT] in Remark 2.3.5, (i), and updated the Bibliography entry  for [BogIUT]