This question was asked in 2020, and had a built-in five day deadline. It never received an answer but did have some helpful comments. Since this is a general question, and future users might benefit from reading an answer, I will try to answer it.
Generally, it's good to start thinking about applications to your next position several months in advance of the first deadlines. That way, you can request letters of recommendation from your professors early, can talk to professors and friends to generate a list of programs to apply to, have plenty of time for things like updating your CV, writing a personal statement, etc., and can make a plan for how to get each application done before its deadline. Some master's degrees feed into PhD positions at the same university, so it's good to tell your advisor early on if you plan to do your PhD elsewhere. In particular, this can help them suggest a suitable course of study and master's thesis topic. Your professors can also help you meet (or reach out electronically to) professors abroad who might be interested to take you on as a PhD student.
As you think about which places to apply, pause for a moment to think about what settings will be most correlated to your happiness, wellness, and sense of fulfillment, because all of these are related to your ability to succeed. Think about where you want to live (e.g., urban vs rural, climate, culture, etc.) It is very easy to find yourself in a setting that contributes to feeling isolated, sad, etc., and it's hard to do good research when you feel that way. Even better if you already have a relationship with the person you plan to work with for your PhD, because that relationship is also critical to success.
Another point is: consider your long-term career plans, including where you want to live/work long term. Sometimes, to get a job in a specific country, it helps to be a citizen and to have gotten your PhD there. It is possible that going abroad for your PhD could have detrimental effects for your planned career. Your advisor is the best person to discuss this with, because it's very country-specific. I can't comment on Sweden specifically, except to say I do know several non-Swedes who have permanent positions in Swedish universities. Canada has some preferential hiring for Canadian citizens but it doesn't seem to matter whether they got their PhD in Canada or not. Also, different PhD programs have different track records for how likely it is that their graduates will get a permanent position and you can usually find info on this online.
Another cultural difference is that some PhD positions in Europe are funded directly by a grant, which means you essentially apply to the professor directly instead of the university. For such applications, it's very helpful if you or your advisor already has a relationship with the person, or if you've had coursework (including reading courses with your advisor) preparing you for that specific person's subject of interest. In contrast, in the USA, you usually apply to the university, then later select your advisor (though, it can be a good idea to mention in your application who you hope to work with, and why you think your background/interests are a good match for that person).
Lastly, in terms of well-known departments in algebra or representation theory, I'd make a list first based on what your advisor and other professors tell you, and then do a bit of Googling. When I do that, it suggests to look at Harvard, Princeton, Yale, Stanford, University of Chicago, etc. But it's good to apply to a variety of places, at different levels of selectivity, so I'd also look at Dartmouth, some of the University of California schools (like UCLA, UCSD, etc.), and some state schools like Ohio State, University of Oregon, University of Washington, University of Illinois-Urbana, University of Kentucky, etc. I'd do more than just look at the research group: I'd look at individual professors and read the introductions to some of their papers, to see if their research program is of interest to you. Frequent conversations with your advisor, regarding your specific interests so far, can narrow down the list a lot. I might aim to apply for 8-15 programs depending on your strength, recognizing that a big part of the acceptance process is random. Good luck!
