I "discovered" a few minutes ago that every poset can be embedded into a meet-semilattice.
Let $\mathfrak{A}$ be a poset. Then it is embedded into the meet-semilattice generated by sets $\{ x \in \mathfrak{A} \mid x \le a \}$ where $a$ ranges through $\mathfrak{A}$.
I'm sure I am not the first person who discovered this. Which book could you suggest to read about such things?
This result is mentioned for example as theorem 1.1 in chapter 1 of J.B. Nation's "Revised Notes on Lattice Theory". See also theorem 2.2 in chapter 2. One advantage of Nation's text is that it is freely available.