If you have bought the game, you can download a stand-alone launcher for Minecraft here.
It will automatically update the game files with the latest version.
You will be able to play the game without an internet connection if you’ve run the launcher at least once while connected to the internet.
Download Minecraft.zip, extract the Minecraft app, then run it.
Linux / Other:
Download Minecraft.jar, an executable jar file. It might work as-is.