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The monograph compiles state-of-the-art approaches in the mathematical modeling of lithium batteries. The chapters of this work deal with electrochemical models, electrochemical impedance spectroscopy models, equivalent circuit models, reduced order models, state-of-charge algorithms, battery thermal models and battery-ageing models for lithium ion batteries in a coherent manner. Starting from fundamental theory, equations, model development, solution methodology to algorithms, this monograph connects fundamental electrochemistry of batteries to controlling processes and eventually to on-board battery state estimators. In addition to detailed discussions of each approaches, this work connects them together, by evolving one approach from more detailed ones.§This work is expected to be of immense benefit for electrochemical or chemical engineers involved with electrode design, control engineers involved in state of charge algorithms, or thermal engineers involved with coolant system design. Given the interest in battery research and applications, till date mathematical modeling has been confined to books specifically written in an area, or in research publications. The present level of maturity of battery modeling techniques warrants a comprehensive monograph that this work aims to fulfil.§