"Algorithms in Algebraic Geometry" is a technical book that focuses on the development and implementation of algorithms for algebraic geometry. Over the past ten years, interest in these algorithms has significantly increased in both abstract algebraic geometry and practical applications. The book documents the outcomes of a workshop held as part of the IMA Annual Program Year in Applications of Algebraic Geometry, which saw numerous participants from various countries. The collected articles provide insights into the diverse problems and algorithms that encompass both symbolic and numerical approaches. This publication is a valuable resource for researchers and practitioners looking to engage with the latest developments in algebraic geometry and its applications.