e access control layers of the overall system. A fundamental challenge is how the mismatch among services with different numerologies affects signal detection, channel estimation, and equalization. In addition, the mismatch will also result in PHY configurations disorder and misalignment among services/slices. This, from the slice level viewpoint, will bring intricate interference. From the resource allocation perspective, such a high degree of heterogeneity among services fosters a complex radio system composed of three resource layers. To address the abovementioned issues, waveforms with low out-of-band emissions are important in multi-service systems, as isolation between the signals corresponding to different services is required. Therefore, there is a common consensus on the need to introduce alternative technologies that complement orthogonal frequency division multiplexing (OFDM) by a more flexible and effective air interface that better serves the challenging requirements of future networks than OFDM. To this end, in the recent years, several candidate waveforms have emerged, e.g., filtered OFDM (F-OFDM), universal filtered multicarrier (UFMC), generalized frequency division multiplexing (GFDM), filter bank multicarrier (FBMC) and orthogonal time frequency space (OTFS) modulation. As one of the pillars that underpins multi-service communications in future networks, the first part of this book presents the recent advances in waveform design and provides an in-depth insight to the reader about different waveforms and their relationship with OFDM. Furthermore, the first part of the book provides a new perspective that facili- tates straightforward understanding of channel equalization and the application of the new waveforms in provision of services with different requirements. It also facilitates derivation of efficient structures for synthesis and analysis of these waveforms. From the mixed numerologies coexistence perspective, the first part of the book will discuss signal detection, channel estimation, e