This document provides an overview of electrochemical machining (ECM) and tool profile correction in ECM. It discusses how ECM works through controlled anodic dissolution at the atomic level using a shaped tool and electrolyte. Material removal rate in ECM is governed by Faraday's laws of electrolysis. The document also examines the dynamics of ECM with and without tool feed, showing that with feed the tool-workpiece gap remains constant. Finally, it provides an example of how tool shape must be corrected to accurately machine complex profiles, developing equations to calculate the needed corrections.