A lot of time is spent in this chapter, among other places, discussing the different categories of “Muktza” and their complex laws.
These involve mainly restrictions on moving items that are not set aside for use on shabbos, for various reasons.
Yet what exactly are the reasons for this myriad of rabbinical restrictions?

On our daf, there is a dispute between Rabbah and Rava as to which categories of items may be moved on shabbos, for different reasons.
Without going into the entire debate, Rava expresses the view that according to Chachamim, a דבר שמלאכתו להתיר (something whose main purpose is permitted on shabbos), may be moved for any reason whatsoever on shabbos, and a דבר שמלאכתו לאסור may be moved לצורך גופו ( if it is needed for a permitted purpose,) לצורך מקומו (if one needs the place that it occupies), but not מחמה לצל (for its own protection.)

Abaya challenges Rava with a Mishna (Beitza 32b) that forbids one to support a pot with a piece of fire- wood.
Firewood is a דבר שמלאכתו להתיר on Yom-Tov, yet we see that it may not be handled even for another permitted use, let alone for the sake of its place or protection!
גזרינן יום-טוב אטו שבת

After a failed first attempt at resolution, The Gemara says that firewood is different because it is a כלי שמלאכתו לאסור on shabbos.
Chazal thus forbade using it for another purpose on Yom Tov in case one comes to use it for a permitted purpose on Shabbos as well. (this in itself seems strange given that it looks like a גזירה לגזירה, but as usual, we have to leave that for another post someday.)

Even though using a דבר שמלאכתו לאסור for a permitted purpose is allowed on Shabbos as well, according to Rava, the Gemara explains that this is only the case if it has תורת כלי (the status of a useful vessel, which a plain piece of wood does not have.)
Something usually used for a forbidden melacha that does not have the status of a כלי may not be used on shabbos even for a permitted purpose.

This in itself is a big chiddush (novel idea) given that the phrases used until now have not been כלי שמלאכתו להתיר and כלי שמלאכתו לאסור but simply דבר שמלאכתו להתיר and דבר שמלאכתו לאסור.
Be that as it is, we see from here that there are times that Chazal forbade things that would ordinarily be permitted on Yom Tov, so one doesn’t come to do them on shabbos. (a phenomenon that needs clear boundaries, given that there are certainly things permitted on Yom Tov that are forbidden on shabbos.)

The Gemara questions the idea that Chazal forbade doing things on Yom Tov because of Shabbos: There is an explicit Mishna that allows one to lower fruits that have been drying out on the roof through a skylight on Yom Tov in case of rain , but not on Shabbos. (the exact issue with this requires further analysis, but it appears from Rashi to have something to do with the exertion involved in it.)

The Gemara immediately brings a counter proof that Chazal do indeed forbid things on Yom Tov because of shabbos, from another Mishna (Megillah 7b) which states that the only difference between Shabbos and Yom Tov is that on Yom Tov, melacha needed for the preparation of food is permitted. This implies that other things not needed for food on Yom-Tov, are forbidden, even if done with something that is a כלי שמלאכתו להתיר on Yom-Tov but not on shabbos.

The Gemara makes several attempts to reconcile the various texts that imply that Chazal made decrees forbidden otherwise permitted things on Yom-Tov out of concern for Shabbos.
מתוך
After an initial failed attempt, the Gemara answers that these different Mishnayot reflect the famous argument between Beis Hillel and Beis Shamai regarding the rule of מתוך.

Beis Shamai holds that even a melacha which is permitted because it is usually performed for the sake of food preparation may only be done for the sake of food, but not for other needs.

Beit Hillel holds that מתוך שהותרה לצורך הותרה נמי שלא לצורך – this means essentially that once a category of melacha is permitted because it is normally associated with food preparation, it becomes permitted for any legitimate Yom Tov need.

For example, lighting a fire is not permitted only for cooking, but also for warming the room or heating water for permitted washing (though rabbinically it may only be lit from an existing flame.)

It follows that Beis Shamai could forbid any handling of items on Yom Tov that are not for the usual purpose of the permitted melacha, namely food preparing, particularly (and perhaps only) whereas Beis Hillel would permit it.

The Mishna that forbids using firewood for another permitted purpose other than cooking thus represents the view Beis Hillel, as does the Mishna which says that the only difference between Shabbos and Yom-Tov is melachos needed for and associated with food preparation.
The Mishna that permits lowering fruit on Yom-Tov but not on Shabbos reflects the view of Beis Hillel.
The Gemara then points out that we have indeed seen that Beis Shamai is stringent about not performing a permitted biblical melacha on Yom Tov for a purpose other than food.

Yet we have not found that they are similarly stringent about the rabbinical prohibition of טלטול (merely moving/handling items in a permitted domain) to the point that he forbids moving them for a purpose other than food.
אסור מוקצה היא גזירה אטו אסור הוצאה

The Gemara concludes that seeing as טלטול itself is משום הוצאה (because of the melacha of taking something out,) Beis Shamai forbade even handling items that one is permitted to use for food, for non-food purposes.
The simple explanation of this seems to be that the entire reason for the rabbinic prohibition of handling Muktza is in order to prevent one from transferring an item he is carrying from one domain to another- in other words , a סייג (fence) or גזירה (decree) אטו הוצאה (because of the melacha of הוצאה.)
As such, anything that one is forbidden to transfer on Yom Tov or shabbos may also not be handled, except for purposes Chazal made allowances for.
As transferring firewood for anything other than food-related needs is forbidden on Yom-Tov according to Beis Shamai, it follows that handling anything other than for its normal permitted purpose is as well.
As Beis Hillel permits transferring any item for any Yom-Tov need on Yom-Tov, they also permit handling it for any purpose.
On Shabbos, when everyone agrees that transferring any item from one domain to another is forbidden, everyone also agrees that handling it is too, unless it is for a permitted purpose.
After quite a long introduction during which we learnt some other important principles, such as the requirement for a דבר שמלאכתו לאסור to be a כלי in order for it to be moved לצורך גופו ולצורך מקומו, and the rule of מתוך on Yom-Tov, we seem to finally have discovered the reason for the decree of Muktza!
This is indeed the way the Ritva understands the Gemara, and though slightly more open to interpretation, Rashi seems to take this approach as well.
שיטת הרמב”ם- The Rambam’s approach
The Rambam, however (Shabbos 24/12-13) suggests several reasons for the prohibition of moving Muktza:

1. So that one does not handle items the way one does during the week, and land up spending shabbos moving items around.
2. In the case of a כלי שמלאכתו לאסור, to prevent one from using it for a forbidden melacha.
3. So that people who are unemployed and hardly do melacha during the week will also have a way of making shabbos special
   Yet the one reason the Gemara brings explicitly, the Rambam seems not to mention!
   The Raavad points this out, and in his usual way, disagrees with the Rambam and accepts the reason given in the simple meaning of our Sugya- that it is simply a decree designed to prevent the melacha of הוצאה.
   Why does the Rambam bring 3 relatively creative reasons of his own and seemingly ignore our Gemara? Did he interpret it differently to us, or does he simply have a contradictory sugya elsewhere that he considers to be more authoritative? Any feedback is welcome.

What is Melacha?

We have learnt before that although the Torah forbids performing any melacha on Shabbos, Chazal derived from the proximity of the prohibition to the work of the Mishkan that only those actions that were done in the process of the mishkan(avot melacha) and things similar to them (toladot) are including in the prohibition.
Does this mean that there are some types of melacha which remain permitted on Shabbos, or that any action that doesn’t fit into the above criteria simply isn’t considered a melacha at all?
There is much to discuss, but it does seem from the Mishna on Daf 124b, that there actions which are called “melacha” but still permitted on shabbos.
The Mishna tells us that one may handle pieces of broken vessels on Shabbos, so long as it is done מעין מלאכה , for the sake of some “melacha.”- in this case, it still has a valid purpose on shabbos, and is not considered “Muktza.”
Rabbi is stricter, and requires that it can still be used for something similar to the “melacha” it was fit for before it broke, such as using a broken pot-cover to cover something smaller- otherwise it is forbidden, (possibly as form of “Muktza” known as “nolad”- see the rest of the daf and daf 125 for the full discussion)
Either way, we see that certain actions performed on shabbos, such as using a lid to cover a pot, are indeed referred to as “melacha” even though they do not fit into the categories of forbidden “melacha”, and are clearly permitted on shabbos!
Whether this is “simply” semantics, or has greater ramifications, invites further analysis.