Capitalize University when it refers to the University of Nevada, Reno (formal name).
This is the official name of the University and should be used on first reference. An exception would be when addressing an audience, such as employees, that would understand immediately what is meant by “the University.” Use of “University of Nevada” is also OK for first reference; “Nevada” and “UNR” are acceptable for second reference.
Include comma, UNLV on second reference.
This is the correct title of University’s fund-raising arm.