I am a newbie using Fedora 13 .I have other users using my system and want to kind of spy on what activities they are doing in my absence.
Can I (administrator)monitor what a user did i.e what did he surf in the net,what files he opened and what he typed etc.
Also it should be hidden from their eyes.In short I want a spyware.

Is this plan too ambitious or is it within my reach?

It is possible and available and it does not need to be labeled "spyware". It can be hidden unless somebody else has root account access, boots from removable media or if it causes errors that can not be contributed to something else. However unless you are talking about a workplace (in which case rules and regulations apply) it is also a violation of other peoples privacy. Snooping on others is generally considered amoral and voyeuristic to boot. I suggest you explain in detail your compelling reasons for wanting to violate other peoples privacy. Thanks in advance.

Snooping is not my certainly not my intention ,nor do I wish to interfere with other users privacy.I run a small internet cafe in my town,there are just about 4 systems in my place but I am doing well.I was compelled to ask such a thing since people have been using internet IN this part of the world to spread terror propaganda ,and in fact at times communicate as well.There is no effective identity system in place by which identities can be co0nfirmed.Fake IDs can be easily made .God forbid if anything happens the internet cafe owner is also roughed up in the investigation.That is why if such a program is in place I can easily see if there has been any suspicious activity.
This is a seemingly compelling reason for such a question,but Respected Moderator if you feel that such an application might be misused by me or any one else please be free to deny me the information.I will appreciate it still.

The best way to combat this would be to avoid situations like that. You need to set and publish rules for 'net access, basically a TOS and state in proper legalese that you retain the right to deny any customer access who violates your rules. With respect to enforcing it, as well as from a risk and maintenance point of view, you'll have to decide on the trade-off. Apart from sites you will want to blacklist regardless of the method, for protocols that can be filtered through say Dansguardian white-listing provides less risk but restricts 'net access considerably, conversely black-listing allows 'net users more freedom but at a greater risk. That leaves you with methods and traffic that can't be filtered for various reasons like encryption (SSL, GnuPG?), proprietary protocols (Skype?) and other means of covert communication. If the risk of finding yourself in a court of law (or worse) over stuff like that is greater than the need to provide customers with less-restricted access then you should block as much as possible and again understand that white-listing trumps black-listing.

* If you want help then saying something like "be free to deny me the information" isn't in your best interest. I suggest you refrain from doing that again unless you also want me to help you with attitude adjustment.