This project brings a brief over view of the principal components of Mathematical Analysis and of a couple of the first concepts in Abstract Algebras. In the field of Analysis it starts from the axioms of Peano and gradually works its way to characterize the natural, rational and real numbers. Some attention is given to the nature of Series and Sequences. And concludes analysis with comments on functions. In the field of Algebra we explore rings, Ideals and Factorization domains.