I don't know what you mean by "nature", but you can probably determine interests by how long they spend on pages of each topic. You need to make a list of all the URLs on your site and categorize each according to whatever topic area they would correspond to, then estimate time spent on each page, where possible, and add together the times for each topic area and sort by time spent.

Also of interest might be average time spent per page and a flowchart of the user's path through the site, and for overall information, it's very useful to know which links people take to visit other pages. For each page you should have a frequency list of links followed to that page, and links followed out of that page.

I'm not going to write it for you, though :)