Structural dynamics is more than just an extension of the static analysis of structures. The presence of time as an independent variable leads to a host of new phenomena, such as resonance, which have no counterpart in statics. It also allows for considering a host of new categories of external forcing functions, such as moving loads, ground motions, blasts, explosions, wind gusts, etc. Furthermore, it opens the way for introducing the frequency domain, which gives new insights into the way vibratory energy is channelled through a structural system. This work aims at providing the reader with knowledge on both basic and advanced topics in the field of vibrations of structural systems, which can be categorized as either discrete or continuous. The emphasis is on numerical methods of solutions, which have been programmed in the Java, resulting in the Symplegma Development Environment (SDE) that forms an integral part of this book. Further reference will be made to numerical solutions based on contemporary discretization techniques ranging from the commonly used finite elements to boundary elements and to more advanced mixed forms. Furthermore, the topic of modal analysis is of central importance to structural dynamics, where the response of the system is captured in the modal space through the use of modal shapes (or eigenvectors) and natural frequencies (or eigenfrequencies). Identification modal analysis, which is often classified as either experimental or operational modal analysis, consists in determining modal characteristics of a given system from a set of measured responses in the form of transient signals. Vibration based methods for localized damage detection which take advantage of machine learning techniques are currently a topic under rapid development because of its relevance to the field of structural health monitoring. Part I of the book focuses on the mathematical background behind modelling structural systems, either as single degree-of-freedom (SDOF) systems or as multiple degree-of-freedom systems (MDOF), or as continuous systems. In Part II, open source software is employed, which was developed mainly in Java language with the Apache Groovy a Java Virtual Machine (jvm) based language serving as the scripting mechanism. This will provide a working platform for the reader to implement the material presented in Part I book and to further explore applications that might be of interest.