Climate modeling and simulation teach us about past, present, and future conditions of life on Earth and help us understand observations about ecology and the atmosphere. Focusing on high-end modeling and simulation of earth's climate, this book presents PDEs used to model weather and climate, covering numerical methods for geophysical flows in more detail than other texts. It also discusses parallel algorithms and high-performance computing for weather and climate simulations, with supplemental lectures and MATLAB exercises on an accompanying website. This book is for graduate students in science and engineering. It is also useful for a range of computational science and engineering researchers who encounter climate models, or those who want a brief introduction to the topic. In particular, the material on numerical methods and using parallel algorithms on high-performance computers will challenge researchers who aim to improve the prediction of climate on decadal to century time scales.