A short introduction to nonlinear vibration and the most basic and common methods for characterizing nonlinear systems experimentally. The lecture discusses the harmonic balance method to introduce the concept of amplitude dependent natural frequency (and damping), introduces nonlinear normal modes, discusses nonlinearities due to bolted joints, and common methods for detecting nonlinearity including the homogeneity test and time-frequency analysis including the spectrogram and zeroed-early-time FFT (ZEFFT).