Üstünde is the preposition 'on': Masanın üstünde bir kitap var. (There is a book on the table) Altında is the preposition 'under': Kedi koltuğun altında. (The cat is under the sofa) They show locative case. And they are always used with genitive case of the previous noun: MasaNIN altında/üstünde. But yukarıda and aşağıda are local adverbs. They show locative case, too. We use them with the verbs like to stay, to be etc. Ali yukarıda. (Ali is upstairs) Ev aşağıda. (The house is beneath) The correct forms of these words; ÜSTÜNDE/ALTINDA - YUKARIDA/AŞAĞIDA

yukarda means up üstünde means it's on top of something aşağinda means it's under something altında means it's beneath something the last two one are a little bit trickier than the first ones.