Any software that covertly gathers user information through the user's Internet connection without his or her knowledge, usually for advertising purposes. Spyware applications are typically bundled as a hidden component of freeware or shareware programs that can be downloaded from the Internet. Once installed, the spyware monitors user activity on the Internet and transmits that information in the background to someone else. ...
While not necessarily malware, adware is considered to go beyond the reasonable advertising that one might expect from freeware or shareware. Typically a separate program that is installed at the same time as a shareware or similar program, adware will usually continue to generate advertising even when the user is not running the originally desired program.
A software program capable of reproducing itself and usually capable of causing great harm to files or other programs on the same computer; "a true virus cannot spread to another computer without human assistance"
A Trojan horse is a program in which malicious or harmful code is contained inside apparently harmless programming or data in such a way that it can get control and do its chosen form of damage, such as ruining the file allocation table or hard disk. A Trojan horse may be widely redistributed as part of a computer virus.
A rootkit will does many things. It will first hide its own process so that AV can miss it. Then it will replace system files to cause damage to Windows. Its main purpose is to gain administrative level privilege on your computer or network. Rootkit are dangerous as it also contains spyware which can steal your personal data.