This book presents the proceedings of the Third IMA Conference on Mathematics of Robotics, held in Manchester in September 2025. It brings together a diverse collection of contributions that reflect the increasing role of mathematics in addressing fundamental problems in robotics. This book covers a wide range of methods including algebraic geometry, control theory, numerical optimisation, and topological data analysis, applied to topics such as kinematics, motion planning, soft robotics, and multi agent systems. The breadth of contributions, both in subject matter and in international participation, highlights the growing global community at the interface of mathematics and robotics. Alongside rigorously reviewed research papers, this book also features keynote lectures addressing themes such as uncertainty quantification and geometric approaches to robotic manipulation. Together, these works provide a valuable reference for mathematicians, engineers, and researchers seeking to advance the theoretical foundations and practical capabilities of robotics.