This course provides an introduction to methodologies and techniques in Data Analytics and Machine Learning, with specific applications to semiconductor manufacturing, from physical design characterization to process and yield optimization. While the growth of (Big) Data Analytics and Machine Learning continues to increase across virtually every industrial sector, the semiconductor space has seen only a modest adoption. This course aims at lowering the entry barrier, by providing both foundational and practical skills for semiconductor engineers and practitioners. Following a comprehensive survey of the state-of-the-art and current developments in Data Analytics and Machine Learning, the course describes how functional interactions and data information flows in the Design-to-Manufacturing chain can be enhanced by analytics algorithmic methodologies. Quantitative definitions of physical design space coverage and process space learning are introduced as the unifying abstraction, allowing for the construction of a computational application framework. Design-Technology-Co-Optimization (DTCO) is then extended with the novel paradigm of DFM-as-Search. Examples from this new DFM computational toolkit, are used to demonstrate how the advanced IC technology nodes (14, 10, 7 and 5nm) not only benefit from, but actually require the use of a new class of correlation extraction algorithms for heterogeneous data sets.