Inter-universal Teichmuller Theory I ------------------------------------ ・Inserted a missing space in the first display of Remark 4.9.1, (i) Inter-universal Teichmuller Theory II ------------------------------------- ・In the second display of Remark 3.6.4, (iv), inserted the word "portion" Inter-universal Teichmuller Theory III -------------------------------------- ・Corrected misprints in the Introduction ("regarded a positive real multiple" ---> "regarded as a positive real multiple",  "but rather with]" ---> "but rather] with") ・Added an additional reference at the end of Remark 3.3.2, (i) Inter-universal Teichmuller Theory IV ------------------------------------- ・In the discussion immediately following the first display of Step (v) of the proof of Theorem 1.10,  replaced the phrase "the tensor product of log-shells under consideration" by more precise notation  (2 instances)