I found out that there exists a search option
intags:mine which only returns posts in your favorite tags. So if you search for
intags:mine is:q you get list of all questions from your favorite tags. You can then order the search results in the way you wish to (recently active, newest, ...)
This seems to be a way simpler solution that the things I have described below. (I did not know about this search option.) Anyway I am leaving those information here, too, as they may be useful for some users.
Per OP's request, I'll post my comment as an answer.
It's not exactly what you want, but you could go to http://stackexchange.com/filters and click on "Favorite tags".
You can also create various other filters there. You can obtain RSS-feed or e-mail notifications from a filter.
That site has one obvious disadvantage that you lose MathJax rendering. One possible solution is use robjohn's bookmarklets or something similar to render mathematics.
Another possibility would be using in-built search. For example, if you search for
[real-analysis] or [general-topology] or [elementary-set-theory], only questions having at least one of these tags are shown. (Here is a link to this particular search.) You can then choose ordering of the search results (for example choose recently active questions or newest questions).
You can do this for your favorite tags. (Or any set of tags you are interested in.) This means that you have to add several tags manually, but if you plan to look at those tags regularly, you only need to do this once and then bookmark the link to the search or save the link somewhere.
There a feature request at meta.SO Tab for questions that are labeled with favorite tags, which is tagged status-declined, but it contains several tips for workarounds.