Most fields require M.S./Ph.D. students to complete one or two minors. Usually each minor is a series of 3-6 graduate courses in a field other than the one in which your degree will be granted. Some fields expect the minor(s) to be in a closely related area to your thesis research, and others allow more latitude when choosing a minor. Sometimes the field has no preference, and approval of the minor is entirely up to the chair of the special committee. In many cases, a M.S. degree requires and allows only one minor; Ph.D. programs may require one or two minors. Be sure to check with your Director of Graduate Studies and your faculty advisor regarding the particular requirements in your area. The list of possible minors is almost endless; some engineering graduate students have been known to minor in modern dance or Russian Literature. These are exceptions, however. Your best resource for advice on this is graduate students in your research group or field and the chairperson of your committee.
M.Eng. students generally do not complete minors, but may choose to complete a ``program option" which is similar to a minor. Most of the available program options require three courses, and the requirements for each option are fairly specific. If you have any questions about completing a program option, see the director of the M.Eng. program in your department.