This is the problem: how can you edit a DVD into a new DVD, either selecting chapters and removing chapters, and then compiling them into a new DVD?

The structure of the DVD is mentioned without detail in this link:
DVD File structure basics
http://www.videohelp.com/dvd

There is also some information on the IFO file here:The DVD would have some format similar to:
The problem is that when playing the DVD on a DVD player, it presents a menu with many chapters/titles to select from but Linux does not seem to display the menu in Totem or Mplayer. And looking at the files with "ls", you can not see what chapters/titles there are. That information is in the IFO files?

The above DVD file structure, has 14 chapters/titles. I would like to be able to get the video and audio from a few selected chapters/titles, and then make a new DVD. The problem is extracting the video and audio from the VOB file using the information in the IFO file. Once I have the video/audio then I can make a new DVD with it. What Linux software tools will allow me to do this? Or, what script will allow me to do this?

I played with this briefly in the past. You might want to look into K9Copy. If I remember correctly, it provides options to keep or remove menu features and chapters.