Existsforall Academy presents a trilogy of books: Rigorous Elementary Mathematics, authored by Samer Seraj. The theme of the books is the rigorous proof of many results that are often learned by students without proof in elementary mathematics, specifically in algebra, counting, and number theory. The books were written for students of mathematical contests and olympiads who want to add a rigorous foundation to their understanding of the theorems that they use, and for teachers and coaches who want to solidify their own fundamentals. The cumulative number of letter-sized pages is 750. The documents are available for free from this webpage. The download links and tables of contents are provided below. To stay up to date on further projects, please sign up for the academy’s Newsletter. You might also be interested in my research Publications.