A deep dive into collaborative document editing algorithms, covering the two primary approaches used in tools like Google Docs. Operational Transformation (OT) is explained through a worked example showing how concurrent edits from multiple users create conflicts, and how a transform function produces adjusted operations (a' and b') that converge all clients to the same document state. Differential Synchronization is also covered, describing how clients and server each maintain shadow copies, compute diffs, exchange patches, and apply them to keep documents in sync. Key design considerations include using a central authoritative server, optimistic concurrency control, acknowledgement-based sequencing of operations, and persisting operation history in a time-series or NoSQL store for conflict recovery.