No case after a preposition, and what je is for

A noun after a preposition stays plain: pri la libro, kun la amiko, sur la tablo. The one exception is movement towards a place: en la domo is in the house, en la domon is into it. Al and el already mean movement, so they never take -n: mi iras al la urbo.

The Fundamento gives every preposition one fixed meaning, then supplies je, which has none, for when the sense you want matches no other. In practice it has settled onto clock time, je la tria horo, a measured difference, je du jaroj pli juna, and a few set phrases. The same rule lets you use a bare accusative instead, so la trian horon means the same thing. Use it sparingly: a preposition with a meaning of its own is usually clearer.

Da follows a word of quantity and links it to the stuff being measured: iom da akvo, peco da pano, multe da homoj. It never takes la after it. De does everything else, meaning possession, origin, and the doer of a passive verb. The test is a single question. Is the first word telling you how much? Then da. Is it telling you whose, or where from? Then de. A bare numeral needs neither, because tri libroj is already complete.