Please explain what a trojan horse is, a worm and a virus and what harm they can do?

Trojan:

In the context of computing and software, a Trojan horse, or simply trojan, is a piece of software which appears to perform a certain action but in fact performs another such as a computer virus. Contrary to popular belief, this action, usually encoded in a hidden payload, may or may not be actually malicious, but Trojan horses are notorious today for their use in the installation of backdoor programs. Simply put, a Trojan horse is not a computer virus. Unlike such malware, it does not propagate by self-replication but relies heavily on the exploitation of an end-user (see Social engineering). It is instead a categorical attribute which can encompass many different forms of codes. Therefore, a computer worm or virus may be a Trojan horse. The term is derived from the classical story of the Trojan Horse.

In the field of computer architecture, 'Trojan Horse' can also refer to security loopholes that allow kernel code to access anything for which it is not authorized.

Other;

Malware is software designed to infiltrate or damage a computer system without the owner's informed consent. It is a portmanteau of the words malicious and software. The expression is a general term used by computer professionals to mean a variety of forms of hostile, intrusive, or annoying software or program code.

Many normal computer users are however still unfamiliar with the term, and most never use it. Instead, ''computer virus'' is incorrectly used in common parlance and even in the media to describe all kinds of malware, though not all malware are viruses.