Mathematics appears to be concerned with abstract objects such as numbers and sets. What are these objects? Oystein Linnebo develops an account of thin or lightweight objects, applicable in mathematics but also more generally, according to which certain objects do not require very much for their existence. This account builds on ideas due to the great logician and philosopher Gottlob Frege (1848-1925). The result is a distinctive approach to ontology, that is, the metaphysical study of what there is. Abstract objects such as numbers and sets are demystified and allowed to exist alongside more familiar physical objects. The account involves a novel approach to set theory (generally regarded as the foundation of all of mathematics) which takes seriously the idea that sets are formed successively.