Note that, to get an idea of the contents, you can see the previously published fascicles, and earlier drafts online (pre-fascicles):
• Mathematical Preliminaries Redux: https://cs.stanford.edu/~knuth/fasc5a.ps.gz
• 7.2.2 Introduction to Backtracking: https://cs.stanford.edu/~knuth/fasc5b.ps.gz
• 7.2.2.1 Dancing Links: https://cs.stanford.edu/~knuth/fasc5c.ps.gz
• 7.2.2.2 Satisfiability: https://cs.stanford.edu/~knuth/fasc6a.ps.gz
The first three were published together as "Volume 4, Fascicle 5" in 2019, and the last one—Satisfiability—was published as "Volume 4, Fascicle 6" in 2015. Of course the actual publication as Volume 4B has hundreds of fixes and additions beyond what was published earlier, and a lovely preface that you can read here: https://www.informit.com/articles/article.aspx?p=3143614
> You might think that a 700-page book has probably been padded with peripheral material. But I constantly had to "cut, cut, cut" while writing it, because […] new and potentially interesting-yet-unexplored topics kept popping up, more than enough to fill a lifetime; yet I knew that I must move on. […] I wrote nearly a thousand computer programs while preparing this material, because I find that I don't understand things unless I try to program them.
• Mathematical Preliminaries Redux: https://cs.stanford.edu/~knuth/fasc5a.ps.gz
• 7.2.2 Introduction to Backtracking: https://cs.stanford.edu/~knuth/fasc5b.ps.gz
• 7.2.2.1 Dancing Links: https://cs.stanford.edu/~knuth/fasc5c.ps.gz
• 7.2.2.2 Satisfiability: https://cs.stanford.edu/~knuth/fasc6a.ps.gz
The first three were published together as "Volume 4, Fascicle 5" in 2019, and the last one—Satisfiability—was published as "Volume 4, Fascicle 6" in 2015. Of course the actual publication as Volume 4B has hundreds of fixes and additions beyond what was published earlier, and a lovely preface that you can read here: https://www.informit.com/articles/article.aspx?p=3143614
> You might think that a 700-page book has probably been padded with peripheral material. But I constantly had to "cut, cut, cut" while writing it, because […] new and potentially interesting-yet-unexplored topics kept popping up, more than enough to fill a lifetime; yet I knew that I must move on. […] I wrote nearly a thousand computer programs while preparing this material, because I find that I don't understand things unless I try to program them.