Learn Russian: Мальчик слез с дерева. - The boy climbed down from the tree.

The preposition с (from, off of) is the exact grammatical counterpart to на (on, onto). Because you climb onto a tree (на дерево), you must climb down from or off of it using с (с дерева). You would only use из (out of) if you were coming out from inside something (в).

The verb слез and the preposition с both feature the letter с. Is that on purpose?

Yes! In Russian, verbs of motion often use a prefix that matches the preposition. The prefix с- on the verb means down from or off of, pairing perfectly with the preposition с to emphasize the exact direction of the movement.

What is the infinitive of слез, and why is this past tense form so short?

The infinitive is слезть (to climb down, to get off). Like many Russian verbs ending in -зть or -сть (such as упасть, meaning to fall), the masculine past tense drops the suffix completely, leaving just the root слез. If the subject were a girl, it would be слезла.

Why does дерево change to дерева?