Current measurement systems depend more and more on mathematical and computational approaches. Novel developments include virtual metrology digital twins, sensor networks, uncertainty quantification of computationally expensive models and artificial intelligence. Altogether, metrology has started to move from consideration of individual devices to more systemic approaches, which are needed to cope with measurement challenges in climate and pollution monitoring, digital health and the factory of the future. Also optimization, inverse problems and sampling methods play a more important role than in the past. This book will start with introducing the basic principles and classical statistical and mathematical models employed in metrology and expand from there, addressing the novel developments mentioned above. This will be done from the perspective of metrology whereby both theoretical and practical aspects are carefully addressed by experts from the field.