As the title of this book suggests, it is about how intelligence may be understood as information compression (IC). More specifically, the book is about the {em SP Theory of Intelligenc} (SPTI) and its realisation in the {em SP Computer Model}---and their potential applications, benefits, and associated ideas. The SPTI draws on substantial evidence for the importance of IC in human learning, perception, and cognition. Since the SPTI also has much to say about issues in artificial intelligence (AI), it is a theory of both natural and artificial intelligence. In the SPTI, IC is achieved largely via the powerful concept of {em SP-Multiple-Alignment}, a major discovery which is largely responsible for the versatility of the SPTI in aspects of human intelligence and beyond. Strengths of the SPTI include: the modelling of several kinds of intelligent behaviour, including several kinds of probabilistic reasoning; the representation and processing of several kinds of intelligence-related knowledge; and the seamless integration of diverse aspects of intelligence, and diverse kinds of knowledge, in any combination. That seamless integration appears to be {em essential} in any AI system that aspires to the fluidity and versatility of human-level intelligence. Related to the SPTI is another major discovery: {em that mathematics may be seen as a set of techniques for IC, and their application}. This suggests the creation of a {em New Mathematics} via the integration of mathematics with the SPTI, combining the strengths of both. The SPTI also suggests new thinking in concepts of probability and new thinking about `computation’, with potential benefits in both areas. The SPTI has been shown in peer-reviewed papers to be relevant to areas not closely associated with AI. These include: the management of `big data'; the development of autonomous robots; medical databases; sustainability of computing; transparency in computing; and computer vision.