This publication contains 29 case studies offering lessons learned during a four year NSF-supported MAA project designed to support mathematicians and mathematics departments in the increasingly important challenge of assessing student learning. Three introductory essays set assessment in broader academic and national contexts; an appendix contains the 2005 revision of the CUPM Guidelines for Assessment of Student Learning. The case studies deal primarily with coherent blocks of courses designed for particular purposes, e.g., general education, math-intensive majors, developmental education, quantitative literacy, teacher preparation, and mathematics majors. Institutions represented in the volume vary considerably in size, location, and mission. The case studies presented here are useful not just for the results achieved, but also to alert those starting assessment programs to the kinds of issues they will need to consider, the potential pitfalls along the way, and strategies for how these can be avoided. The range of solutions represented in these case studies offers readers a large variety of models to adapt to their own institutions' needs. Three articles comprise the introduction: (1) Tensions and Tethers: Assessing Learning in Undergraduate Mathematics (Bernard L. Madison); (2) Asking the Right Questions (Lynn Arthur Steen); and (3) Assessing Assessment: The SAUM Evaluator's Perspective (Peter Ewell). The 29 case studies are: (1) Assessment of Developmental, Quantitative Literacy, and Precalculus Programs (Bonnie Gold); (2) Assessing Introductory Calculus and Precalculus Courses (Ronald Harrell and Tamara Lakins); (3) Mathematics Assessment in the First Two Years (Erica Johnson, Jeffrey Berg, and David Heddens); (4) Using Assessment to Troubleshoot and Improve Developmental Mathematics (Roy Cavanaugh, Brian Karasek, and Daniel Russow); (5) Questions about College Algebra (Tim Warkentin and Mark Whisler); (6) Assessing the General Education Mathematics Courses at a Liberal Arts College for Women (Abdel Naser Al-Hasan and Patricia Jaberg); (7) Assessment of Quantitative Reasoning in Applied Psychology (Robert R. Sinclair, Dalton Miller-Jones, and Jennifer A. Sommers); (8) Assessing Quantitative Literacy Needs across the University (M. Paul Latiolais, Allan Collins Zahra Baloch, and David Loewi); (9) Precalculus in Transition: A Preliminary Report (Trisha Bergthold and Ho Kuen Ng); (10) An Assessment of General Education Mathematics Courses' Contribution to Quantitative Literacy (Aimee J. Ellington); (11) Assessment of Mathematics-Intensive Programs (Dick Jardine); (11) Developing a Departmental Assessment Program (William O. Martin and Dogan Comez); (12) Assessing the Use of Technology and Using Technology to Assess (Alex Heidenberg and Michael Huber); (13) A Comprehensive Assessment Program--Three Years Later (Kenneth B. Hannsgen); (14) Assessment of a New American Program in the Middle East (Thomas W. Rishel); (15) Assessment of Mathematics Programs to Prepare Future Teachers (Laurie Hopkins); (16) Assessment in a Middle School Mathematics Teacher Preparation Program (Bonnie Gold); (17) Using Practice Tests in Assessment of Teacher Preparation Programs (Jerzy Mogilski, Jorge E. Navarro, and Zhong L. Xu); (18) Assessing the Undergraduate Major in Mathematics (William A. Marion); (19) Learning Outcomes Assessment: Stimulating Faculty Involvement Rather Than Dismay (Dan Kalman, Matt Pascal, and Virginia Stallings); (20) The Development, Implementation, and Revision of a Departmental Assessment Plan (Barbara M. Moskal); (21) Assessing Student Oral Presentation of Mathematics (Dick Jardine and Vincent Ferlini); (22) Keeping Assessment Simple (Jesus Jimenez and Maria Zack); (23) Surveying Majors in Developing a Capstone Course (M. Paul Latiolais, Joyce O'Halloran, and Amy Cakebread); (24) Assessing Written and Oral Communication of Senior Projects (Kevin Dennis); (25) Assessing the Mathematics Major: A Multifaceted Approach (Brian Hopkins, Eileen Poiani, and Katherine Safford); (26) Assessing the Mathematics Major through a Senior Seminar (Donna Flint and Daniel Kemp); (27) Assessment of Bachelors' Degree Programs (James R. Fulmer and Thomas C. McMillan); (28) Assessment of the Undergraduate Major without Faculty Buy-in (Edward C. Keppelmann); and (29) Assessing the Mathematics Major with a Bottom-Up Approach (Sarah V. Cook). The publication concludes with: SAUM Assessment Workshops; and SAUM Project Steering Committee. Appended is: CUPM Guidelines for Assessment of Student Learning.