This book covers recent advances in the method used in testing, especially in the case of structural integrity that includes fatigue and fracture tests, vibrations test and surface engineering tests that are extremely crucial and widely used by engineers and industries. The book will provide you with information on how to apply the advanced formulation, advanced theory and advanced method of testing that are relevant to all engineering fields: mechanical, electrical, civil, materials and surface engineering. The topics are explained comprehensively, including the reliable test that one should perform in order to effectively investigate the strength and validation of the developed theory or model. I hope that the material is not too theoretical and that the reader finds the case study, formulation, testing method and the analysis helpful for tackling their own engineering and science based studies.