Three consonants hold one idea and its mirror: to learn and to teach. In the light pa'al mould the root means "learn" (take knowledge in); intensify it into pi'el and the very same letters mean "teach" (push knowledge out). From that single hinge spread the pupil, the lesson, the scholar, and the most famous derivative of all, the Talmud. Nothing below is memorized separately. They are the same three letters seen from different angles. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Watch the hinge: pa'al לִלְמֹד is "learn" (take in), but its intensive pi'el לְלַמֵּד flips to "teach" (give out). The nif'al is the passive of that act, a subject "gets taught". The matching passives pu'al and huf'al exist in the system but are not lexicalized here, and the hif'il is not used: Hebrew already has a dedicated "teach" in the pi'el, so it does not need a causative one. That is normal: not every root fills all seven binyanim.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.