Perhaps you read a Swedish translation of Up the Line, a 1969 novel by Robert Silverberg. As a two-part serial in the July 1969 and September 1969 issues of Amazing Stories, it is available at the Internet Archive. A Swedish translation of Up the Line, titled Tidsströmmen (Timestream), was published in 1979 in Kindbergs Förlag's Alpha Science Fiction series; it's ISBN 91-85668-09-5 according to The Quasi-Official Robert Silverberg Web Site Majipoor.com. There is a review of Tidsströmmen in Swedish at Svenssongalaxen.
There is no time travel to the future; otherwise it seems to be a good match for your description.
Wikipedia plot summary:
Jud Elliott II is a failed Harvard history masters student in 2059. Bored with his job as a law clerk, he takes up a position with the Time Service as a Time Courier.
After an introductory course, Jud shunts up and down the time line ("up the line" is travel into the past; "down the line" is forward time travel, but only to "now-time," Jud's present of 2059) as a guide for tourists visiting ancient and medieval Byzantium/Constantinople.
Jud's problems include not only stupid tourists, but also greedy and mentally unstable colleagues who attempt to cause various types of havoc with the past. He is forced to break the rules in order to patch things up without drawing the attention of the Time Patrol.
When he meets and falls in love with the 'marvelous transtemporal paradox called Pulcheria' - his own multi-great grandmother - Jud succumbs to the lure of the past, creates irreparable paradoxes, and faces the inescapable clutches of the Time Patrol.
Silverberg's narrative includes some cleverly worked out details about the problems of time-travel tourism. For example, the number of tourists who over the years wish to witness the Sermon on the Mount has increased the audience at the event from the likely dozens to hundreds and even thousands.
Time-tour guides re-visiting the same event must also take care not to scan their surroundings too closely, lest they make eye contact with themselves leading another tour party.
Silverberg's interest in the Byzantine era of Roman history is put to use with a vivid description of Constantinople during the reign of Justinian, and the Nika riots of 532.
Excerpt (a lecture at time-travel school):
"I spoke the other day of cumulative audience paradox. This is a severe
philosophical problem which has not yet been resolved, and which I will
present to you now purely as a theoretical exercise, to give you some insight
into the complexities of our undertaking. Consider this: the first
time-traveler to go up the line to view the Crucifixion of Jesus was the experimentalist Barney Navarre, in 2012. Over the succeeding two decades another fifteen or twenty experimentalists made the same journey. Since the commencement of commercial excursions to Golgotha in 2041, approximately one
tourist group a month, or 100 tourists a year, has viewed the scene. Thus
about 1800 individuals of the twenty-first century, so far, have observed the
Crucifixion. Now, then: each of these groups is leaving from a different
month, but every one of them is converging on the same day! If tourists
continue to go up the line at a rate of 100 a year to see the Crucifixion, the crowd at Golgotha will consist of at least 10,000 time-travelers by the middle of the twenty-second century, and, assuming no increase in the permissible tourist trade, by the early thirtieth century some 100,000
time-travelers will have made the trip, all of them necessarily congregating simultaneously at the site of the Passion. Yet obviously no such crowds are present there now, only a few thousand Palestinians—when I say 'now,' I mean of course the time of the Crucifixion relative to now-time 2059—and just as obviously those crowds will continue to grow in the centuries ahead of
now-time. Taken to its ultimate, the cumulative audience paradox yields us the picture of an audience of billions of time-travelers piled up in the past to witness the Crucifixion, filling all the Holy Land and spreading out into Turkey, into Arabia, even to India and Iran. Similarly for every other significant event in human history: as commercial time-travel progresses, it must inevitably smother every event in a horde of spectators, yet at the original occurrence of those events, no such hordes were present!
How is this paradox to be resolved?"