What learning mechanisms are available to infants on the cusp of language learning? One learning mechanism that young infants can exploit is statistical in nature. For example, Saffran et al. (1996) found that the looking behaviors of eight-month-old infants indicated a sensitivity to statistical information inherent in sequences of speech sounds produced in an artificial language, e.g., transitional probabilities. In this talk, I will review evidence collected in my lab which shows that infants also have a second learning mechanism available, one that allows them to learn abstract, "algebraic" rules -- open-ended abstract relationships that can be freely generalized to arbitrary instances.