What types of swords were used by the crusaders and their main enemies-the saracens? I'm interested in both historical examples, information and technical stuff like crossections etc.
Thanks!

Which Crusade? 1st - 8th? It matters, as there was a lot of evolution of arms & armour during the course of the Crusades.

1st-4th, but I'm mainly interested in the 1st one

As for European swords from the 1st to 4th crusade, you should start by looking at Oakeshott types X and XI. If you go to the features section of this sight you'll find good articles on both these types of sword.

!st to 4th Crusades - from late 11th to early 13th centuries. Look at the sword type described here - http://myArmoury.com/feature_oakeshott2.html

Also, have a look at Alfred Geibig's typology which is different from Oakeshott's. A simplified version of it can be found here: http://myArmoury.com/feature_geibig.html. Following the simplified typology, Type 5, 6, and 7 swords probably would have been most common during the First Crusade. Type 6, 7, 8 and 9 would have been most common during the Second Crusade, while Type 8, 9, 10, 11 and 12 would have been most common for the Third Crusade and Fourth.

For the first crusade interests of European arms and armor, I think the Bayeux tapestry is going to offer the best visual reference, its from about the same time period separated by only a few dozen years.

References for Asia minor I cannot remember off hand, and I'm not up to my reading anymore. What I can state, is that during the time of the first crusade the Turks did not yet adopt a curved blade, so they looked similar to European arms. The closest relative to these early Turkish swords, may be Ethiopian and north African cuneiform swords.

Families X and XI mainly, with XII and XIII coming in for the last few decades. Type Xa is probably the archetypal sword of the high middle ages.

Swords on both sides would have looked rather similar in the beginning. If anything, curved swords would have been most likely to be found in Byzantine hands, and possibly some of their Seljuk opponents -- but in any case curved blades would have been pretty unusual on either side during the early Crusades. Have a look at some of the examples here:

https://myArmoury.com/talk/viewtopic.php?t=17520