Our planet faces many challenges. In 2013, an international partnership of more than 140 scientific societies, research institutes, and organizations focused its attention on these issues. This project was called 'Mathematics of Planet Earth' and featured English- and French-language blogs, accessible to non-mathematicians, as part of its outreach activities. This book is based on more than 100 of the 270 English-language blog posts and focuses on four major themes: A Planet to Discover; A Planet Supporting Life; A Planet Organized by Humans; and A Planet at Risk. Readers will learn about the challenges that confront the Earth today, and how mathematics and mathematicians can contribute to a better understanding of these challenges. This book is accessible to a general audience with a basic scientific background. Mathematicians will learn about some planetary challenges which provide mathematical and/or interdisciplinary research problems.