The Multiple Mirror Telescope (MMT) has been used in experiments with sodium laser guide stars to sense and correct atmospheric image distortion. The major goal was to develop and test concepts for a full adaptive optics system, to be used in two years when the present array of six 1.8-m telescopes will be replaced with a single 6.5-m mirror. The guide star, produced by a con- tinuous-wave dye laser beam projected out along the optical axis of the telescope, was as bright in the V band as a natural star of mv = 10.4. Our tests culminated in the first demonstration of a sodium laser guide star used to improve the image of an astronomical telescope, in this case formed by two of the six 1.8-m apertures. Two adaptive servo loops were closed simultaneously. The laser beacon provided a measure of the differential wavefront tilt between the two apertures, and a natural guide star was used to measure the overall wavefront tilt. A factor of two improvement in the K-band Strehl ratio was measured, and the resolution improved from 0 ".58 to 0".41. The experiment dem- onstrated all the features needed for correction of the 6.5-m telescope to the diffraction limit using a sodium beacon. The accuracy with which the laser beacon measures the atmospheric aberration of starlight across the full 6.9-m aperture of the MMT was examined. This was done with the artificial beacon and a coaxial natural star, and using the six elements of the MMT as a large Shack-Hartmann wave- front sensor to measure the shape of both wavefronts simultaneously. The small difference be- tween the wavefronts, caused by focus anisoplanatism, was analyzed in terms of Zernike coefficients, and was found to correspond to a Strehl ratio of 77% in the K band over the full ap- erture sampled, despite poor seeing during this measurement. From more extensive measurements of binary star wavefronts, we deduce that focus anisoplanatism for the 6.5-m telescope will corre- spond to a Strehl ratio of typically 88% at K under normal seeing conditions. In a laser-based adaptive system, a natural guide star is still required to sense overall wavefront slope. Our measurements of binary stars also yielded the image degradation to be expected from differences in the overall slopes between the wavefronts from the object of scientific interest and the natural guide star. A Strehl ratio of 80% at K was deduced for an offset of 40 ", implying that good sky coverage will be possible. In general our results are consistent with calculations based on measurements of atmospheric turbulence at the best sites. Our direct measurements over such a large aperture show clearly the effects of a finite and variable outer scale of turbulence. Subject headings: atmospheric effects - techniques: image processing - turbulence