The (publishing) world is a bit strange in this regard. Sometimes internal tentative dates end up in xls sheets that in turn end up in places like Amazon and become real before they are. The 3rd edition is still being worked on and my plans/hopes is to be ready for copy-editing early next year, i.e. February timeframe. From that point on it will still take several months until publication date, so summer 2022 is what I think is realistic.
And just to prove that "something" is happening here are the latest draft covers (from December 2021):


They aren't the final ones but we are getting closer.
Update July 2022
We are now in the middle of copy editing and proof reading by the publisher (as well as preparing the final index). Volume I is essentially done, but finishing Volume II + index will take us to January in the current schedule. In other words my optimistic assumption above was simply too optimistic: I should have done the math and figured out how much work it is to copy-edit 20 chapters, each of which with an average of 80-90 pages.
Somebody asked below if a TOC is available. The answer is yes, here are the draft TOCs for both volumes:
Update November 11th, 11:11, 2022
More or less exactly at that moment (which is a very important day+time in my city, because then the fifth season starts) I have finished the last copyedit corrections for the book, so it is soon going into the production phase. Paper selection was made (same as Don Knuth's for his TAOCP series) --- this is difficult these days, good paper is a rare thing. There are a few outstanding bits and pieces to be resolved for the production, but we are well in front of the original schedule, so I hope that the planned publishing date (which was April/May 2023) can be moved earlier. If there is an update I will post that here.
Happy and tired :-)
Semi-final update January 2nd, 2023
Between the previous update and today the remaining work was done at my end: yet another two rounds of checking the index to make it better and dealing with final organizational questions like the cover blurb, legal pages, etc. At 2AM on Christmas Eve I was finally able to send of camera-ready copy to the publisher and now it is out of my hands.
Im sorry to say, that it is still not yet with its own page on the publisher's shop informit.com, but I hope we get that sorted during the next weeks and also sad is the fact that odering information on various online shops are still inaccurate (often only listing the first part and not the bundle of part I+II). The reason is that initially only one volume was planned and even though the change to two has been communicated long ago, it seems difficult to get the old data weeded out. Anyway, here is the final info on ISBNs:
Part I:
ISBN-13: 978-0-13-465894-0
ISBN-10: 0-13-465894-9
Part II:
ISBN-13: 978-0-201-36300-5
ISBN-10: 0-201-36300-3
Part I+II: (bundle)
ISBN-13: 978-0-13-816648-9
ISBN-10: 0-13-816648-X
but in all honesty it doesn't make much sense to buy the parts individually or only one of them --- it is really a single book but because of its size (1984 pages in total) split into two equal volumes and the bundle is supposed to be noticeably cheaper than the individual books.
In a few days all examples from the book are available for download from https://ctan.org/pkg/tlc3-examples (I will upload them to CTAN tonight).
Given that I managed to finish a month or so earlier than planned I have some hope that the publishing date moves earlier too, but who knows ... in any case I will make a final update when that happens.
Final update March 8th, 2023
As mentioned in a comment by Jacques Cremer the third edition is now listed on the publisher's website, InformIt, as ready for preordering. The printed version is with the printer so the publication date will be met to the best of my knowledge (and just for the record, as this isn't always mentioned correctly: the books are hardcover with reading ribbons).
The digital version is in the works with a vendor generating an ePub version. There is a good chance that that will be ready by beginning of May, but if I'm not happy with the results then there might be a bit of delay (the uPDF was prepared by me and is with the publisher
so that is already ready).
Note, that the InformIt bundle offering is unique and not available elsewhere (containing the books + uPDF + ePub). Same with the digital only offering which contains uPDF + ePub. On other platforms, e.g., Amazon, you only get the ePub as the digital product, because they don't sell it in several format (I think that's a pity but this is how they operate).
So here is the offical publisher link to it
The full set of examples from the edition are available from CTAN at
including both the sources and the pdf output.
Finally, I'm going to update the material on our website during the next days so that one can take a look at a comprehensive selection of sample pages there (basically the first pages of each chapter). This will show up (probably by the weekend) at