The Advanced Photon Source (APS), a new synchrotron radiation facility being built at Argonne National Laboratory, will provide the world''s most brilliant x-ray beams for research in a wide range of technical fields. Successful operation of the APS requires an extremely stable positron closed orbit. Vibration of the storage ring quadrupole magnets, even in the submicron range, can lead to distortion of the positron closed orbit and to potentially unacceptable beam emittance growth, which results in degraded performance. This paper presents an overview of the technical approach used to minimize vibration response, beginning at the conceptual stage, through design and construction, and on to successful operation. Acceptance criteria relating to maximum allowable quadrupole magnet vibration are discussed. Soil properties are used to determine resonant frequencies of foundations and to predict attenuation characteristics. Two sources are considered to have the potential to excite the foundation: far-field sources, which are produced external to the facility, and near-field sources, which are produced within the facility. Measurements of ambient ground motion, monitored to determine far-field excitation, are presented. Ambient vibration was measured at several operating facilities within Argonne to gain insight on typical near-field excitation sources. Discussion covers the dynamic response characteristics of a prototype magnet support structure to various excitations, including ambient floor motion, coolant flow, and magnet power.