Understanding Exposure is practically from another era, first published in 1990. Pro cameras didn't have multi-segment metering (Matrix for Nikon, Evaluative for Canon) until 87/88, so he's likely referring to center-weighted/partial metering modes. I personally don't think much of that book.
Matrix metering is the "auto-everything" of metering modes. It sets your exposure for you. If that's what you want then use it, but I'm perplexed at why you'd be reading a book like Understand Exposure. Spot metering is the mode for people who want total control over exposure. However, the problem with controlling exposure is that you have to actually do it...you have to be able to set the desired exposure if you want your images to come out right. If you read the book you should get some idea of how to do this.
Just a note...there's no benefit to shooting in manual. Manual is good for times when the meter doesn't work, as with astrophotography, long exposure photography, and certain types of flash photography. But with modern auto mode functionality, if the meter works then manual mode is the wrong mode. You'll get more from an auto mode. Also, the shooting mode has nothing to with setting exposure or anything to do with the metering mode. All techniques used to determine correct exposure are equally valid in Program mode as they are in manual mode. It truly means nothing to be shooting in manual mode.