Textbook in PDF format In computational acoustics, standard Finite Element Methods (FEM) face severe limitations when modelling high-frequency wave propagation. As the wavenumber increases, fixed discretization levels lead to rapid growth in pollution error, rendering standard solutions inaccurate. This book addresses this critical challenge by exploring advanced discretization strategies, including high-order polynomial-based Finite Elements, Isogeometric Analysis (IGA) using Non-Uniform Rational B-Splines (NURBS), and Enriched Finite Elements incorporating oscillatory basis functions (Partition of Unity). Beyond homogeneous media, the text extends these high-order approximation techniques to heterogeneous acoustic environments with spatially varying wave speeds. It details the mathematical foundations of pollution error quantification, the construction of enriched basis functions, and the performance of preconditioned iterative solvers. This book is an essential resource for engineers and researchers seeking to overcome the limitations of classical FEM in industrial acoustic applications