This document provides a comprehensive overview of modal analysis theory and testing, authored by Ward Heylen, Stefan Lammens, and Paul Sas from the Division of Production Engineering, Machine Design and Automation at Katholieke Universiteit Leuven, Belgium. Part A covers the theoretical foundations of modal analysis, including analytical and experimental approaches, signal processing, modal parameter estimation, model validation, and the use of modal parameters. It discusses single and multiple degree of freedom systems, their equations, transfer functions, poles, natural frequencies, damping ratios, and modal vectors. The text also explores signal processing techniques such as Fourier transforms, Laplace and Z-transforms, and various signal analysis parameters. Modal parameter estimation methods are detailed, including peak picking, mode picking, circle fitting, and several frequency and time domain methods. Model validation techniques like modal scale factors, modal assurance criterion, and mode participation are explained, along with model updating, reduction, and expansion techniques. Correlation methods, parameter selection, and correction methods are also covered, with examples and practical applications. The document concludes with appendices and references, providing a thorough resource for understanding and applying modal analysis in engineering.This document provides a comprehensive overview of modal analysis theory and testing, authored by Ward Heylen, Stefan Lammens, and Paul Sas from the Division of Production Engineering, Machine Design and Automation at Katholieke Universiteit Leuven, Belgium. Part A covers the theoretical foundations of modal analysis, including analytical and experimental approaches, signal processing, modal parameter estimation, model validation, and the use of modal parameters. It discusses single and multiple degree of freedom systems, their equations, transfer functions, poles, natural frequencies, damping ratios, and modal vectors. The text also explores signal processing techniques such as Fourier transforms, Laplace and Z-transforms, and various signal analysis parameters. Modal parameter estimation methods are detailed, including peak picking, mode picking, circle fitting, and several frequency and time domain methods. Model validation techniques like modal scale factors, modal assurance criterion, and mode participation are explained, along with model updating, reduction, and expansion techniques. Correlation methods, parameter selection, and correction methods are also covered, with examples and practical applications. The document concludes with appendices and references, providing a thorough resource for understanding and applying modal analysis in engineering.