LVM is grouse.

It works like this :-

file systems:       /home   /var/log
logical volumes:    /dev/mapper/main-homes  /dev/mapper/main-varlog
volume groups:              main
physical volumes:   /dev/sda1   /dev/sdb1   /dev/sdc1


LVM is partition type 8e

To display all of the available block storage devices that LVM can 
potentially manage:-

sudo lvmdiskscan
Output
  /dev/ram0  [      64.00 MiB] 
  /dev/sda   [     200.00 GiB] 
  /dev/ram1  [      64.00 MiB] 

  . . .

  /dev/ram15 [      64.00 MiB] 
  /dev/sdb   [     100.00 GiB] 
  2 disks
  17 partitions
  0 LVM physical volume whole disks
  0 LVM physical volumes


..or pvscan - also makes partitions available to the OS :-

sudo pvscan
  PV         VG          Fmt  Attr PSize   PFree 
  /dev/sda   LVMVolGroup lvm2 a--  200.00g     0 
  /dev/sdb   LVMVolGroup lvm2 a--  100.00g 10.00g


..pvdisplay is easier to look at :-

sudo pvdisplay
Output
  --- Physical volume ---
  PV Name               /dev/sda
  VG Name               LVMVolGroup
  PV Size               200.00 GiB / not usable 4.00 MiB
  Allocatable           yes (but full)
  PE Size               4.00 MiB
  Total PE              51199
  Free PE               0
  Allocated PE          51199
  PV UUID               kRUOyU-0ib4-ujPh-kAJP-eeQv-ztRL-4EkaDQ

  --- Physical volume ---
  PV Name               /dev/sdb
  VG Name               LVMVolGroup
  PV Size               100.00 GiB / not usable 4.00 MiB
  Allocatable           yes 
  PE Size               4.00 MiB
  Total PE              25599
  Free PE               2560
  Allocated PE          23039
  PV UUID               udcuRJ-jCDC-26nD-ro9u-QQNd-D6VL-GEIlD7


To discover the logical extents that have been mapped to each volume, pass in the -m option to pvdisplay:

sudo pvdisplay -m
Output
  --- Physical volume ---
  PV Name               /dev/sda
  VG Name               LVMVolGroup
  PV Size               200.00 GiB / not usable 4.00 MiB
  Allocatable           yes 



--
add a new partition to a volume group with these :-

..first create a volume group to use :-

pvcreate /dev/sdb1

extend the existing volume group using the space you just created with :-

vgextend ubuntu-vg /dev/sdb1

..vgs should show that it is bigger now.

now grow the logical volume :-

lvextend -l +100%FREE /dev/ubuntu-vg/root

resize the filesystem with :-

resize2fs /dev/mapper/ubuntu--vg-root

..enjoy your extra space.
  PE Size               4.00 MiB
  Total PE              51199
  Free PE               38395
  Allocated PE          12804
  PV UUID               kRUOyU-0ib4-ujPh-kAJP-eeQv-ztRL-4EkaDQ

  --- Physical Segments ---
  Physical extent 0 to 0:
    Logical volume  /dev/LVMVolGroup/db_rmeta_0
    Logical extents 0 to 0
  Physical extent 1 to 5120:
    Logical volume  /dev/LVMVolGroup/db_rimage_0
    Logical extents 0 to 5119

   . . .
--

ubuntu, and redhat/centos has a gui called system-config-lvm

--
resizing

..you can reduce a lvm logical volume _and_ the filesystem that is on it with :-

lvreduce -L 2048G --resizefs /dev/mapper/cl_melbpm108-home

..you _could_ do this in two steps by shrinking the filesystem with resize2fs (and shrinking a little 
more that you need to) - then lvreducing the logical volume - then resize2fsing the fs to really fill
up that volume - But all modern lvm distributions seem to have --resizefs - so why would you ?

..you cant resize xfs. Well - you sort of can, but you shouldnt.

umount /home
e2fsck -f /dev/mapper/cl_melbpm108-home
fstransform /dev/mapper/cl_melbpm108-home ext4
e2fsck -f /dev/mapper/cl_melbpm108-home
lvreduce -L 2048G --resizefs /dev/mapper/cl_melbpm108-home
e2fsck -f /dev/mapper/cl_melbpm108-home
fstransform /dev/mapper/cl_melbpm108-home xfs
mount /home

..For a file system with a few gig of data, and a few TB of space, the fstransforms take a long time. Hours.
twice. It was MUCH quicker to tar up the filesystem, lvremove the volume, lvcreate a new one, mkfs.xfs a new 
file system, and untar the tarfile back in place. Still - that is only practical if you have space space on
machine, or a sufficiently quick network.