Ultra reliable and low latency communications (URLLC) theory and practice : advances in 5G and beyond Pursuing ever higher data rates has been the central design goal in all the previous generations of mobile communications. This has been changed in the fifth generation (5G) mobile communications that aim to support various new emerging services with diverse and stringent quality of service requirements. The most formidable challenge in 5G is to achieve ultra reliable low latency communications (URLLC) for many mission critical services including autonomous vehicles industry automation and tele robotic surgery i.e. the roundtrip delay of 1 millisecond and less than 1 out of a million in packet loss. In the fourth generation (4G) systems the average latency is usually a few hundred milliseconds and the packet loss probability is around 1%. 5G systems need to significantly improve the latency and reliability by several orders of magnitude compared to 4G systems. This presents unprecedented challenges. This book covers a range of topics from fundamental theories to practical solutions in URLLC. In Chapters 2 and 3 the authors analyze the statistical features and tail distributions of wireless channel and provide useful insights on the performance of URLLC. Chapter 2 presents the statistical aspects of URLLC in both frequentist and Bayesian approaches. The authors have analyzed the statistical features and guarantees for outage probability in a narrowband wireless channel. Chapter 3 considers various metrics of URLLC including tail distribution higher order statistics extreme events with very low occurrence probabilities worst case metrics and reliability latency. The authors have introduced readers the entropic risk measure in financial mathematics generalized extreme value and generalized Pareto distribution to investigate these metrics. From Chapter 4 to Chapter 7 the authors introduced several techniques to guarantee the reliability and latency of URLLC including machine learning candidate channel codes sparse vector coding and network slicing. Two problems of resource allocation in URLLC are addressed in Chapter 4 with an unsupervised learning approach. The results have shown that bandwidth utilization efficiency of URLLC can be improved more significantly by exploiting frequency diversity than by multi user diversity. Chapter 5 discusses the channel coding and decoding schemes for URLLC. This chapter reviews state of the art channel codes for URLLC and analyzes them in terms of performance and complexity. Furthermore the ordered statistics decoding (OSD) is promoted as one of the potential universal decoding algorithms for URLLC. In Chapter 6 a new approach to support short packet transmissions referred as sparse vector coding (SVC) is introduced. The numerical evaluations and performance analysis validate the proposed SVC technique is highly effective in URLLC transmissions. Chapter 7 studies CoMP enabled RAN slicing system simultaneously supporting URLLC and eMBB services. The authors address a joint bandwidth and CoMP beamforming optimization problem to maximize the long term total slice utility. In Chapters 8 and 9 downlink orthogonal frequency division multiple access systems (OFDMA) and full duplex relay system are optimized for URLLC respectively. Chapter 8 investigates the beamforming design for downlink ODFMA to enable the stringent delay requirement. In particular the authors address a non convex optimization problem to maximize the weighted system sum throughput subject to quality of service (QoS) of URLLC users. Chapter 9 presents an up to date overview of the end to end latency for a full duplex (FD) relay system in the context of URLLC. The authors not only provide an insightful investigation of reliability and latency together for FD relay assisted URLLC but also discuss possible relaying latency reduction solutions in the chapter. In Chapters 10 and 11 the authors investigate URLLC in vertical industries: Tactile Internet and Industrial Internet of Things. More specifically Chapter 10 addresses an optimization problem that maximizes the number of URLLC services by jointly optimizing time and frequency resources and the prediction horizon. The numerical results clearly demonstrate the effectiveness of the proposed solution. In addition a proof of concept experiment with the remote control in a virtual factory is also provided to illustrate a typical application of Tactile Internet. Finally Chapter 11 considers relay robots aided URLLC in 5G factory automation which consists of multiple relay robots deployment and decoding error probability minimization problems. There are two different approaches introduced for relay robots deployment including deep neural networks (DNN) and the K means clustering algorithm. A low complexity iterative algorithm is also provided to deal with the joint blocklength and power allocation problem to minimize the decoding error probability