Q:

Half-Life Deathmatch order

Does the Half-Life: Deathmatch and Half-Life 2: Deathmatch go in any order or are they just literally a deathmatch with no meaningful story?
I want to know before I begin playing the series

A:

Half-Life 2: Deathmatch (and the original Half-Life deathmatch multiplayer mode) have no canonical connection whatsoever to the plot of the Half-Life series. 
They are simply there to let you beat random people on the internet with crowbars.

