Next-generation wireless networks are designed to address high delay and Doppler (DD) scenarios for achieving ubiquitous connectivity. However, the performance of current waveforms, such as orthogonal frequency division multiplexing (OFDM), degrades in high-mobility scenarios due to significant Doppler effects. In this chapter, we highlight the fundamentals of the orthogonal time-frequency space modulation (OTFS) system, including its basic principles and block-level implementation. We also discuss the relationship between various communication systems, such as time domain, frequency domain and DD domain. Additionally, this chapter focuses on the OFDM-compatible OTFS system, referred to as the two-stage OTFS system.