Inter-universal Teichmuller Theory I ------------------------------------ ・Replaced the phrase "topological module(s)/monoid(s)" by the phrase "ind-topological module(s)/monoid(s)" in  \S I2 (3 instances); Example 5.1, (v) (2 instances); Definition 5.2, (v) (1 instance), (vi) (2 instances) ・Corrected misprints ("cf.," ---> "cf.") in Remark 3.2.1, (i); the second paragraph of the proof of Corollary 5.3 ・Deleted the words "topological", "discrete" preceding the word "pseudo-monoid(s)" in Definitions 5.1, (v) (4 instances);  5.2, (vi) (4 instances), (viii) (1 instance) ・In the final display of Definition 5.2, (vi), replaced the phrase "topological field" by the phrase "ind-topological field" ・Updated the entries for [JP] and [AbsTopIII] in the Bibliography Inter-universal Teichmuller Theory II ------------------------------------- ・Corrected misprints ("cf.," ---> "cf.") in the third paragraph of the Introduction; Definition 1.1, (i) (four instances);  Remark 1.5.1 ・Replaced the phrase "topological (sub)module(s)/monoid(s)" by the phrase "ind-topological (sub)module(s)/monoid(s)" in  Example 1.8 (16 instances); Remark 1.11.1 (8 instances); Remark 1.11.2, (i) (2 instances); Remark 1.11.3, (ii) (1 instance);  Proposition 3.4 (8 instances); Corollary 3.5, (i) (1 instance); Corollary 3.7, (ii) (3 instances); Proposition 4.1  (4 instances); Proposition 4.2 (4 instances); Remark 4.2.1 (1 instance); Corollary 4.5, (v) (4 instances); Remark 4.7.2  (1 instance); Definition 4.9 (2 instances) ・Corrected misprints ("Remark 5.12.1" ---> "Remarks 5.12.1, 5.12.2") in Remark 3.6.4, (i) (three instances) ・Replaced the phrase "topological abelian groups" by the phrase "ind-topological abelian groups" in Corollary 4.5, (ii)  (1 instance) ・Corrected a misprint ("structure of an" ---> "structure of a") in Remark 4.5.3, (ii), (c) ・Replaced the phrase "topological G-modules" by the phrase "ind-topological G-modules" in Definition 4.9, (i) (1 instance) ・Updated the entry for [AbsTopIII] in the Bibliography Inter-universal Teichmuller Theory III -------------------------------------- ・Replaced the phrase "topological (sub)module(s)/monoid(s)" by the phrase "ind-topological (sub)module(s)/monoid(s)" in  the Introduction (1 instance); Definition 1.1, (iii) (1 instance), (iv) (2 instances); Remark 1.1.1 (3 instances);  Proposition 1.2, (vi) (3 instances); Proposition 2.1, (iv) (1 instance); Proposition 3.1 (2 instances); Proposition 3.2  (3 instances); Proposition 3.5, (ii), (c) (1 instance) ・Replaced the phrase "topological field(s)" by the phrase "ind-topological field(s)" in Definition 1.1, (i) (3 instances);  Proposition 3.1, (i) (3 instances), (ii) (4 instances); Remark 3.1.1, (i) (1 instance); Proposition 3.3, (ii) (1 instance) ・Replaced the phrase "topological ring(s)" by the phrase "ind-topological ring(s)" in Proposition 1.2, (ii), (1 instance);  Proposition 3.1, (i) (2 instance), (ii) (3 instances); Proposition 3.3, (ii) (1 instance); Remark 3.9.1, (i) (1 instance) ・Corrected a misprint in Remark 1.5.1, (ii) ("elements of (G,G)" ---> "elements of G\times G") ・Corrected a misprint in Remark 2.1.1, (ii) ("cf.," ---> "cf.") ・Updated the entry for [AbsTopIII] in the Bibliography Inter-universal Teichmuller Theory IV ------------------------------------- ・Updated the entry for [AbsTopIII] in the Bibliography