How to install XnViewMP in Ubuntu 18.04 and later

1. Download the AppImage file from the XnViewMP homepage.

2. Give it execute permissions.

   chmod +x XnView_MP.glibc2.17-x86_64.AppImage
   

3. Run it.

   ./XnView_MP.glibc2.17-x86_64.AppImage
   

4. To remove, delete the AppImage file and config folder at $HOME/.config/xnviewmp/

1. Download and install the XnView MP deb file from the XnView Homepage. Although there were problems in Ubuntu 16.10, the newer versions (XnViewMP 0.9x) work fine in 18.04 and probably later. XnConvert also worked for me.

Update 19.04 and later (Thanks to Charles Green):
The XnViewMP .deb file does not install needed library libopenal1.

To fix this open a terminal windows (e.g. ctrl+alt+t) and enter the command

sudo apt install libopenal1

2. Install it as **flatpak** from Flathub. Follow the instructions from flatpak.org including the Software Flatpak plugin to setup flatpak including flathub support. After a system restart, you can find XnView and XnConvert in the Software Center and install it from there.

3. As AppImage, see other answer.

XnViewMP is also available as a snap:

~$ snap search xnview
Name      Version     Publisher  Notes  Summary
xnviewmp  0.90-snap1  vs         -      XnView MP is the enhanced version of XnView Classic.

Install with

sudo snap install xnviewmp

Update June 2019: Obviously XnViewMP has been removed from the snap store (I don't know if temporary or permanently), so this will not work anymore, please use one of the suggestions in the other answers.