Anyone with a computer science degree should have learned the necessary components of volume 1, such as data structures, and the fundamental components of the science of computers (assembler, math related to programming, routines, etc). Volume 2 is semi numerical algorithms (math related to programming), which I simply skipped and did not read over. Sorting and searching though, contains the heavy duty theory of algorithms, that make up the core of many (if not most) computer programs. The author estimates that most running time of computer programs is spent sorting and searching (though this book was written in the 60's, I'm sure this still holds true for the most part today).
I'm not saying people should skip volume 1, although they may just want to skim it if they have a CS degree. But sorting and searching is the most relevant to what those who already understand computer science need to know. Also to note, volume 4 is not complete, I think only the first half of volume 4 is done, and was only completed in 2005 by Knuth.