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This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. The book gives an introduction to the most important models of the field, followed by a detailed description of numerical techniques for the models. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers. The results presented in the book will be of particular interest to researchers in bioengineering and computational biology, who face the challenge of solving these complex mathematical models efficiently. The book will also serve as a valuable introduction to a new and exciting field for computational scientists and applied mathematicians.