We study Laver algebras, a class of finite algebras freely generated by a single element satisfying the left self-distributive law. We characterize the necessary and sufficient conditions under which one Laver algebra embeds into another, and we analyze the direct limit of such embeddings, yielding an infinite Laver algebra. We further establish that there exist continuum many non-isomorphic countable Laver algebras. Among them, the direct limit of the classical Laver tables—first introduced by Richard Laver in the 1980s—appears as a particular case.