Tensor network methods are powerful theoretical tools with applications across a range of fields, including quantum physics and artificial intelligence. This accessible text provides a logical, self-contained route into the mathematical framework of tensor networks, presented with unified notation. The inclusion of the necessary prerequisites in linear algebra and quantum mechanics make it accessible for learners from a range of fields. Beginning with matrices, tensors, contractions, and tensor decompositions, it builds the quantum and lattice-model foundations needed to understand modern tensor network methods. Readers are then guided through concepts such as matrix product states, canonical forms, entanglement, time-evolution algorithms, density matrix renormalization group methods and renormalization techniques. The final chapters connect these ideas to machine learning, including probabilistic modelling, generative learning, and quantum artificial intelligence. Designed for graduate-level study, the book's confident explanation, supported by extensive diagrams and exercises, will equip students and researchers with the practical skills for research.