Modulation is the process whereby message information is embedded into a message waveform for transmission over a communication channel. Some types of modulation are implemented in baseband, not having a radio frequency (RF) carrier as in impulse radio or ultra wideband (UWB) communication systems. However, most communication systems are carrier modulated, using a microwave or millimeter wave carrier, where the message information is embedded in the amplitude, frequency, or phase of the RF carrier, or their combination. The chapter begins with a vector space representation of digitally modulated waveforms, including orthogonal expansions, signal space representations, the Gram-Schmidt procedure for obtaining an orthonormal basis and signal vectors, and the properties of signal vectors. Basic binary modulated waveforms are considered, such as binary phase shift keying (BPSK) and binary frequency shift keying (BFSK). This is followed by nonbinary modulation, including M-ary phase shift keying (MPSK), M-ary orthogonal frequency shift keying (MFSK), pulse amplitude modulation (PAM), and quadrature amplitude modulation (QAM). The chapter concludes with Nyquist pulse shaping, including raised cosine and root-raised cosine pulse shaping, and the power density spectrum of the aforementioned digitally modulated waveforms.