The chapter on one page: what to remember, the commands to have at your fingertips, and flashcards for quick revision.
The chapter in eight sentences
LVM stacks flexible layers on top of disks: physical volumes (PV) make up a volume group (VG), from which logical volumes (LV) are cut and given file systems or swap.
Build with pvcreate, vgcreate, lvcreate -n NAME -L SIZE VG (or -l 50%FREE), then mkfs and mount; the device is /dev/VG/LV.
Inspect with pvs, vgs, lvs (and -o +devices) and lsblk -f; the a in the LV Attr means active, o open.
Grow with lvextend -r -L +SIZE LV (or -l +100%FREE), while mounted; the -r also runs xfs_growfs or resize2fs.
A full group needs a new PV: pvcreate, then vgextend VG PV.
ext4 can be shrunk offline with lvreduce -r -L SIZE LV; XFS cannot be shrunk at all. Back up first.
Replace a disk online: vgextend (new), pvmove OLD NEW, vgreduce VG OLD, pvremove OLD.
Make volumes permanent with /dev/VG/LV (or UUID) in /etc/fstab; an inactive volume is fixed with lvchange -ay, and the layout is saved by vgcfgbackup.