This text grew out of the lecture notes from the author at the University of Windsor and was originally copyrighted in 1975. It is now published by the Trillia Group, a publishing company started by his son-in-law, Bradley Lucier, a professor of mathematics and computer science at Purdue. The level of the book is appropriate for a rigorous analysis course. The author writes in the introduction that “we try to simplify the modern Bourbaki approach to make it accessible to sufficiently advanced undergraduates.”