The TAIPEI 101 skyscraper (508-m) is comprised of 101 floors above ground and five floors below ground. It is located in the Hsinyi District of Taipei, Taiwan. The skyscraper is equipped with a 660-metric-ton tuned mass damper - the largest of its type in the world. Both the skyscraper and the tuned mass damper swayed during Typhoon Fanapi on 19 September 2010. Maximum vertical, E-W, and N-S displacements measured on the 90^th floor were approximately 0.26, 4.71, and 9.04 cm, respectively. The spectra of three-component seismograms recorded at the 74^th and 90^th floors above ground and the fifth floor underground are analyzed. Fundamental and higher mode vibrations, with local peak amplitudes, can be clearly seen on the spectra recordings. The frequency of the fundamental mode is about 0.15 Hz, which is the natural frequency for the skyscraper. The fundamental mode of torsional vibration is at about 0.23 Hz. The vibrations observed are actually the combination of translational and torsional vibrations. The two kinds of vibrations of the TAIPEI 101 skyscraper can be observed and identified either from spectral amplitudes of accelerations or from rotational motions.