Inter-universal Teichmuller Theory III -------------------------------------- ・Slightly modified the discussion of "-|log({\underline{\underline \Theta}})|" in the final portion of the Introduction ・Slightly modified the phrasing of the discussion of "possible log-volumes" in the final portion of the Introduction ・Slightly modified the phrasing ("monoid" ---> "[multiplicatively written] monoid") in the discussion of the groupification  at the beginning of Definition 1.1 ・Eliminated the unnecessary superscript "temp" from the notation introduced at the beginning of Proposition 1.2, (vi) ・Slightly modified the discussion surrounding the term "algebraic" in Remark 2.1.1, (ii) ・Slightly modified the discussion surrounding the term "coordinates" in Remark 2.1.2, (ii) ・Corrected a misprint ("structures structures" ---> "structures") in Remark 2.3.3, (iii) ・Added a supplementary explanatory phrase to the discussion of "arbitrary iterations" in Remark 2.3.3, (vi) ・Added a clarifying expression ("[\in Z]", 5 instances) to the term "order(s)" as it is used in Remark 2.3.3, (vi), (viii),  and Fig. 2.5 ・Corrected a misprint ("fundamental incompatible" ---> "fundamentally incompatible") in Remark 2.3.3, (vi) ・Added a new item (ix) to Remark 2.3.3 and renumbered the previous item (ix) as item (x); added a corresponding row  (the bottom row) to Fig. 2.5 that reflects the content of the newly added item (ix) Inter-universal Teichmuller Theory IV ------------------------------------- ・Added a few supplementary comments to the final portion of Remark 2.3.3