Are there any issurim involved in organizing a photo album on Shabbat? Sources would be great if possible.
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The big question is borer and it is a machloket (debate) whether it applies to large objects.
The Aruch HaShulchan Siman 319:8-9 holds that sorting large objects like clothes and silverware is not an issue of borer and completely permitted.
The Shmirat Shabbat kHilchata disagrees and prohibits sorting large objects. (for example see Chapter 3 Borer-89)
Pictures that you don't frame are probably a kli shemelachto lheter, an object whose function is permitted, and you can move them for a permitted function, to protect them or for the space they are occupying. As such, the muktze discussion doesn't really apply. Incredibly valuable pictures (where you put them in frames and designate a place for them and would refrain from moving them), might be muktze machmat chesron kis). See Shulchan Aruch, the beginning of Siman 308, for a definition of muktze machmat chesron kis.