This volume examines the question "Do abstract objects exist?", presenting new work from contributing authors across different branches of philosophy. The introduction overviews philosophical debate which considers: what objects qualify as abstract, what do we mean by the word "exist" and indeed, what evidence should count in favor or against the thesis that abstract objects exist. Through subsequent chapters readers will discover the ubiquity of abstract objects as each philosophical field is considered. Given the ubiquitous use of expressions that purportedly refer to abstract objects, we think that it is relevant to attend to the controversy between those who want to advocate the existence of abstract objects and those who stand against them. Contributions to this volume depict positions and debates that directly or indirectly involve taking one position or other about abstract objects of different kinds and categories. The volume  provides a variety ofsamples of how positions for or against abstract objects can be used in different areas of philosophy in relation to different matters.