Plagiarizing Wikipedia: "Jean-Éric Pin is a French mathematician and theoretical computer scientist known for his contributions to the algebraic automata theory and semigroup theory." He will also be our featured guest in a week, presenting The Generalized Star Height Problem. In advance of his talk, he requested that the audience familiarize themselves with some basic mathematical definitions, such as "monoid" and "completion of a metric space". To which end, I prepared a presentation, went through some light-weight peer review with random friends from the PL group at Northeastern, and then delivered this talk. This is a fun little review on various useful topics in math, and also, a good refresher if you intend to attend Dr. Pin's talk. I hope you enjoy!