The book consists of contributions by plenary speakers and other speakers at the ICOSAHOM 2023 which was held at Yonsei University, Korea during Aug 14-18, 2023 .  The subjects of the book focus on recent advances on the analysis and applications of spectral and high-order methods. In particular, it  includes several survey papers which provide reviews of recent progresses and descriptions of future directions in the related subjects. The book will be of interest to scientists and engineers who are interested in numerical analysis and scientific computing, particularly spectral and high-order methods.