Question

Which type of security threat installs to a computer without the user's knowledge and then monitors all computer activity?

Answer 1

This is called spyware, so I'd say it would be a Trojan Horse, since those can install without alerting anything really.

Answer 2

That would be what is known as Spyware, a common form of this is known as a "Trojan Horse". This type of malware is typically latched on and hidden within files, such as when downloading a pirated version of a song, game, art-work, etc...