The book is called The Mind Illuminated, and is an absolutely fantastic book on meditation. Super cheap too: https://www.amazon.com/Mind-Illuminated-Meditation-Integrati...
I am intrigued to practice the Dalai Lama's usual practice of analytical meditation (listed in parent's linked paper alongside Vipassana), but it's certainly an advanced practice. Most resources I can find recommend a daily practice of Shamatha for some months before undertaking analytical meditation.
I found this poetic description of the thought process one might go through during analytical meditation: https://www.lotsawahouse.org/tibetan-masters/mipham/wheel-of...
I don't know how similar it is, but I was recently part of a "mindful lunch" at work. We all (3 + the person leading) had lunch in a small conference room in silence. We were told to concentrate fully on the food we were eating the texture, taste, smell, sound, and generally experience it as fully as possible. It was even suggested (and I went with it) to put your silverware down with each bite to give it as full of your attention as possible. It was an incredibly interesting experience to be sure.
I’ve been practicing their 18 minute meditation for almost a year and it has been quite amazing.
Where does transcendental meditation fall?
But it's not the only one, and shouldn't be called merely "meditation" without regard to the vast body of practices that exist.
Another form of meditation that's traditionally talked about in Buddhism is shamatha, which translates to something like "concentration" or "tranquility." In this type of practice, the meditator works with a meditation object, commonly the breath, but possibly a sound, mental image, etc. The meditator learns to stabilize the mind and remain fully aware of the object, and in the process learns to debug the mechanisms that direct (and destabilize) conscious attention.
A recently published book called _The_Mind_Illustrated_ by John Yates is fa fantastic resource for this kind of practice.
If you're interested in scientific attempts to categorize and study meditation, the Center for Healthy Minds at UW-Madison does some fantastic neuroscience & psychology research.
https://centerhealthyminds.org/assets/files-publications/Dah...
In the scientific terminology that is emerging these days, Attentional, Constructive, and Deconstructive types of meditation are mapped onto various types of traditional practices (there's a handy chart in the paper).