This is the static position member of the triad, applicable to solids.

Compare to:

	Ágihoz megyek. I am going to(wards) Agi.
	Áginál vagyok. I am at/by (the house of, or stood by) Ági.
	Ágitól jöttem. I came from (the house of, or being next to) Ági.

Application of this case implies that an object is solid and that you are not (going towards/coming from) inside it.

One important thing to note is that one cannot be "inside" members of the solids group. This means that if you say itt `vagyok efy bulinál I here at a party, it means you are stood next to the party, i.e. you are outside the building. You are not in the party.
Buliban vagyok I am in the party, this means you're a guest and are inside the house.

This means "by, at", but do not fall into the trap of using it to mean "in" like we would in English. I'm at a party must be translated to I'm in a party.

This is used for "at the house of next to, adjacent to".

• Áginál vagyok most. I'm at Ági ('s house) now.
• Kinél lesz a buli? Nálatok? At who (whose house) will the party be? At yours? (pl?)

We use the nál- pronouns, especially nálunk, to convey round our way.

• Angliában adunk ájándékokat szülestésnapra. - Mi is. (To a Hungarian:) In England, we give gifts for birthdays. - We too (do the same)
• Nálunk mindig friss a kenyér, uram. At ours (i.e. in this shop) the bread is always fresh, sir.

This case is used to mean on in the context of about your person.

• Van gyufa nálad? Do you have a match on you?
• Kinél van a könyv? Áginál? Who has on them the book? Does Ági?
• Sajnos nincs nálam elég pénz. Unfortunately, I don't have enough money on me.

The final meaning of this case is THAN in comparisons.

• Ági okosabb nálam. Ági is smarter than I.
• Ági nem magasabb nálad. Ági is not taller than you.
• Ő nem szebb Áginál She is not prettier than Ági.

Note that we can only use this form in comparative statements, in which this form of the pronoun replaces mint in its than form. It cannot be used in equality statements because it cannot replace mint in its as form.
Thanks to Sárándi István for his explanation of this subtle point.

The case is explained in more detail here: Comparative adjectives.