May one fix broken glasses and are they considered Muktzah?
Lens came out: It is forbidden to reinsert the lens into the frame even loosely. However, the lens itself is not considered Muktzah unless it shattered or the glasses have broken to the point they are no longer useable. The frames however are Muktzah unless 1) One had worn it this way before Shabbos, or 2) the lens has shattered and thus can no longer be fixed or 3) It is very difficult to reinsert the lens, such as if one lost the screw or if the screw broke and cases of the like.
Plastic glasses: If the lens of plastic glasses popped out on Shabbos, it is forbidden to reinsert it even though it can be easily done. However, there are Poskim who are lenient if this had occurred once before Shabbos and one reinserted the lens before Shabbos, and now this reoccured. Furthermore, some Poskim even initially allow reinserting a plastic lens being that they do not consider this a proper fastening of parts as the parts can be very easily attached.
Eyeglass temple [part which rests on the ear] detached from frame: If the eyeglass temple became detached from the glasses due to a loose screw it is forbidden to reinsert the screw even lightly. Furthermore, it may not be fastened using a safety pin, twist tie and the like. The actual temple/handle that dislocated from the glasses is not Muktzah. However the glasses themseleves, some Poskim rule it is Muktzah. Other Poskim rule that if only one temple became disconnected, the eyeglasses is not Muktzah. According to all, the eyeglasses are not Muktzah in any of the following cases: 1) One had worn it like this before Shabbos, or 2) The temple is broken and thus can no longer be reattached or 3) It is very difficult to reinsert the handle, such as if one lost the screw or if the screw broke and cases of the like, then.
If the nose piece broke off: If the nose piece came off the glasses, although it is forbidden to reattach it, nevertheless, both the glasses and the nose piece are not Muktzah unless a) the nose piece is broken and cannot be reattached, in which case it becomes Muktzah, or b) the glasses can only be worn with difficulty due to the loss of the nose piece, in which case the glasses are Muktzah.
Bending the glasses back into shape: It is forbidden to bend the bent frame of glasses back into shape on Shabbos due to the Biblcial prohibition of Tikkun Keli.
 Admur 313/19 [firmly] 313/21 [even loosely]
The reason: If one inserts it strongly he transgresses a Biblcial prohibition of Tikkun Keli. [Admur 313/19; Michaber 313/6 and 9] It is forbidden to even insert it loosely is due to a Rabbinical decree that one may come to insert it firmly and transgress a Biblical prohibition of Building/Tikkun Keli. [Admur 313/21; Rama 313/6; Ashel Avraham Mahdurah Tinyana; Betzeil Hachachmah 6/123; Sheivet Halevy 6/32; Az Nidbaru 8/33; Imreiy Yosher 1/202; SSH”K 15/77]
Other opinions: Some Poskim rule one may weakly attach the parts of an object together. [Chazon Ish] Accordingly, one may weakly attach the lens to the frame. [Tzitz Eliezer 9/28; Cheilek Leivi 101; Beis Yisrael Landau 12 that one may loosely put it in without tightening the screw]
 Imrei Yosher 1/202; SSH”K 15/77; Yesod Yeshurun 4/129; Piskeiy Teshuvos 313/5
The reason: If both the frame and lens are intact, the lens does not become Muktzah, as it is similar to the case of doors that have detached from their vessel which are not Muktzah, as rules in 308/34; Michaber 308/8; Shabbos 122b.
 The reason: If the glasses [i.e. frame] have completely broke to the point they cannot be used until fixed, it would appear that even the lens would be Muktzah. This is not similar to the door case in which we rule the ddetached door is not Muktzah, being that the object that the doors were attached to is still usable even on Shabbos. Here however, neither the lens or the glasses have a use. Despite this however, one can also say that since they can be re-fixed they are not Muktzah and that is the reason for permitting to move the door of vessels. Vetzaruch Iyun
 Piskeiy Teshuvos 313/5
The reason: Since it if forbidden to fix the glasses on Shabbos they are therefore Muktzah to use out of fear that one may come to fix it, just as we rule regarding a bench that lost a leg. [See Admur 308/47; Michaber 308/16; Shabbos 138b]
 Admur 308/47; Rama 308/16; Beis Yosef 313 regarding a bench with a detached leg that was used before Shabbos
 As in such a case it is similar to the case that the leg broke as opposed to simply became disassembled, in which we rule the bench is not Mukztah [Admur ibid; Taz 308/14; M”B 308/69]
 Piskeiy Teshuvos 313/5; Implciation of Admur ibid who rules we do not suspect one will make a new leg for the bench
 Shraga Hameir 3/43; See Admur 313/19 [firmly] 313/21 [even loosely]
 Betzeil Hachachmah 6/123
 Tzitz Eliezer 9/28; Az Nidbaru 8/33
 As explained above regarding a popped lens
 Kanah Boshem 1/19
 The reason: As it is difficult to wear the glasses without ojne temple and thus it is no different than a lens which has popped out, in which case the glasses become Muktzah to use.
 Az Nidbaru 8/33
 Piskeiy Teshuvos 313/5; Implication of Admur; See sources and explanation brought regarding the previous case of lenses
 Piskeiy Teshuvos ibid, Upashut