Which spells is Rubick unable to steal?

Rubick's ultimate 'Spell Steal' is highly remarkable, since it can steal almost all abilities from any hero.

I know that there are a few abilities that cannot be stolen at all by Rubick, such as Alchemist's Aghanim's Scepter Synth. The Dota 2 wiki does't list abilities that cannot be stolen at all by Rubick's ultimate.

Could you give list of non-passive abilities that cannot be stolen at all by Rubick's ultimate?

Solution 1:

The wiki does talk about the limitations of Rubick's spell steal, and it does provide a list of spells Rubick cannot steal:

Cannot steal passive abilities, item abilities, or active attack modifiers (except for Walrus PUNCH!).

Cannot steal spells which have no use on their own (aka sub-spells, such as Launch Fire Spirit or Shadow Poison Release). Sub-spells are always stolen with their main spell. Some sub-spells when cast allow their main spell to be stolen, while some have no effect.

Can only steal from heroes (including clones, excluding illusions).

Cannot steal the following spells: Quas, Wex, Exort, Invoke, Assimilate, Mischief, Morph, Walrus Kick, Mortal Strike and Vampiric Aura.

To explain why Rubick cannot steal Aghanim's Scepter Synth:

Aghanim's Scepter has an active ability for Alchemist, allowing him to cast it on allied heroes (excluding hero clones and illusions).

When equipped by Alchemist, the scepter itself gains this ability. So Alchemist's Aghanim's Scepter Synth is an item ability, not a spell. This is why Rubick cannot steal it.

Solution 2:

You can steal all active hero abilities with Rubick's ulti. However, there are some abilities which doesn't give you the full utility of the skill.
Devour(Doom's first skill): You can eat creeps and get bonus gold but you won't get the abilities of the creep.
Chronosphere(Faceless Void's ulti): You can use Chronosphere but Faceless Void won't get frozen inside your chrono.
Useful page for Spell Steal interaction