This text has been written in such a way that makes the self study of the IB Mathematics Analysis and Approaches HL course possible. The authors have distilled the fundamental theory into concise explanations and worked examples before providing well constructed problems, ranging from the practicing the mathemtical mechanics of a concept to its higher order applications such in difficult problem solving questions. In doing so, the text adequately prepares the reader to understand the course material and appreciate the applied and pure aspects of mathematical theory. In some cases, particularly on the chapter of differentiating and integrating the Maclaurin Series, the notation used in text deviates from what is most commonly found on IB papers. Here, while the text maintains the use of sigma notation, examination papers tend to use polynomial representation. Overall, this text sets a gold standard for writing textbooks which align with the demands of the course. The worked solutions companion publication is a must have, particularly for understanding and developing the intuition of solving the more challenging questions.