How to check LVM physical volumes, volume groups, and logical volumes in Linux

See the LVM stack at a glance. pvs lists physical volumes, vgs the volume groups, and lvs the logical volumes; the *display commands show the same with more detail.

# Summaries
sudo pvs
sudo vgs
sudo lvs

# Detailed views
sudo pvdisplay
sudo vgdisplay <vg>
sudo lvdisplay <vg>/<lv>

# Free space in a volume group
sudo vgs -o vg_name,vg_size,vg_free