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Many issues of contemporary importance in climate science can be explored using techniques from mathematics and statistics. This timely textbook introduces students and researchers to the conceptual models that capture important aspects of the Earth's climate system and the mathematical and statistical techniques that can be applied to their analysis. Topics covered include the Earth's energy balance, temperature distribution, ocean circulation patterns such as El Nino, and the carbon cycle. Among the mathematical and statistical techniques presented are dynamical systems and bifurcation theory, Fourier analysis, conservation laws, regression analysis, and extreme value theory. Each chapter ends with exercises, making this book ideal for advanced undergraduates and beginning graduate students in the mathematical sciences who are familiar with linear algebra, calculus, and basic statistics. It will also appeal to applied mathematicians and statisticians in academia, national laboratories, and public service organisations.