The evolution of mobile communication networks has always been accompanied by the advancement of inter-symbol interference (ISI) mitigation techniques, from equalization in 2G, spread spectrum and RAKE receiver in 3G, to OFDM in 4G and 5G. Looking forward towards 6G, by exploiting the extremely large spatial dimension brought by large antenna arrays and multi-path sparsity of millimeter wave (mmWave)/Terahertz channels, we propose a novel ISI mitigation technique, termed delay alignment modulation (DAM). The key ideas of DAM are path delay pre-compensation and path-based beamforming, i.e., by deliberately introducing symbol delays to compensate respective multi-path delays of the channel, so that with appropriate per-path-based beamforming, the multi-path signal components will arrive at the receiver simultaneously and constructively. To gain some insights, we first show that perfect delay alignment can be achieved to transform the time-dispersive channel to time non-dispersive channel, without sophisticated channel equalization or multi-carrier processing. This thus enables efficient equalization-free single-carrier transmission or CP-free OFDM transmission. When perfect DAM is infeasible or undesirable, we propose the generic DAM technique to significantly reduce the channel delay spread. This thus provides a new DoF to combat channel time dispersion for more efficient single- or multi-carrier signal transmissions. As an illustration, we propose the novel DAM-OFDM technique, which may save the CP overhead or mitigate the PAPR and CFO issues suffered by conventional OFDM. We show that DAM-OFDM involves joint frequency-domain and time-domain beamforming optimization, for which a closed-form solution is derived. Simulation results show that the proposed DAM-OFDM achieves significant performance gains over the conventional OFDM, in terms of spectral efficiency, BER and PAPR.