The Mathematical Association of America's Committee on the Undergraduate Program in Mathematics (CUPM) is charged with making recommendations to guide mathematical sciences departments in designing undergraduate curricula. "Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide, 2004" is based on four years of work, including extensive consultation with hundreds of mathematicians and more than one hundred members of partner disciplines. Many recommendations in "CUPM Guide, 2004" echo those in previous CUPM reports, but some are new. In particular, previous reports focused on the undergraduate program for mathematics majors, although with a steadily broadening definition of the major. "CUPM Guide, 2004" addresses the entire college-level mathematics curriculum, for all students, even those who take just one course. This guide calls on mathematicians and mathematics departments to rethink the full range of their undergraduate curriculum and co-curriculum to ensure the best possible mathematical education for all their students, from liberal arts students taking just one course to students majoring in the mathematical sciences. The guide presents six general recommendations to assist mathematics departments in the design and teaching of all of their courses and programs. It also contains supplementary recommendations for particular student audiences. The following are appended: (1) The CUPM Curriculum Initiative; (2) The Curriculum Foundations project; (3) Data on numbers of majors; (4) Data on student goals, department practices, advanced courses; (5) Summary of recommendations; and (6) Sample questions for department self-study. An index is also included. (Contains 4 tables.) [This guide was also supported with funding from the Calculus Consortium for Higher Education.]