This article was first written in December 2003 for
the BeezNest technical website (http://glasnost.beeznest.org/articles/99)
LVM [
1]  is a great system to resize filesystems and partitions online [
2], do online snapshots of  the filesystems, span filesystems and partitions on multiple drives. It  is the ultimate solution to the disk space allocation nightmare.
Linux's 
LVM is closely inspired by 
HP-UX, which  provided the technology to 
AIX also. They share almost the same  schemes, functionalities and names for tools and everything else.
Terminology
You will need some knowledge of the terminology of an 
LVM before using it; all 
Volume Managers use a same basic principles  but use sometimes different names.
Volume Group is a "container" that holds 
physical  disks and 
logical volumes. It's wise to only have two volume  groups, a 
VGROOT and a 
VGDATA. 
AIX calls it  a 
diskgroup, since it holds physical disks as well as 
logical  volumes. Example: /dev/datavg/var
Physical Volume is in fact a 
slice or 
partition.  These devices are the building blocks for a 
volume group. Example:  /dev/hdb1
Logical Volume is a part of a 
volume group. The  
logical volume will be supplied with a file system and then can  be mounted. You can also keep logical volumes 'RAW' and assign them to  an Oracle system for example.
Physical Extend (PE) A 
logical volume can be  extended or shrunk with a certain amount of PE's. In AIX this is known  as 
PP. Always be careful with shrinking volumes! Do not shrink  a volume thoo much that it lands into your filesystem; your filesystem  will be immediately an irreversibly useless. Also notice that most filesystems  can grow but not all of them can shrink.
HOWTO
The reference document in this respect is the 
LVM HOWTO.
Here is how to use 
LVM on a Debian Woody, for non-root  filesystems (it is not hard to adapt, though):
Install the needed packages
$ sudo apt-get install lvm10
Prepare the system
# vgscan
Create the LVM partition container
# cfdisk /dev/hda
Use 
8E(LVM) as partition type code.
Create the Physical Volume
# pvcreate /dev/hda4
Create and activate the Volume Group(s)
# vgcreate my_volume_group_name /dev/hda4
# vgchange -a y my_volume_group_name
Create the Logical Volumes
to be continued…
[
1] Kernel 2.6 calls it 
Device-Mapper instead of 
LVM
[
2] read: while programs are running on it