This deposit contains: A summary of 7 equivalent formulations for relativistic velocity addition: 5 using Unit [Real] Quaternions as Velocities, 2 using Four-Velocities expressed as Biquaternions. Several of the "Quaternionic" formulas can already be found (alongside their geometric Compass-and-Straightedge Construction) in [doi:10.5281/zenodo.18322428] (2014) and [doi:10.5281/zenodo.18320378] (2015). A partial draft (first 109 pages) of a forthcoming monographic work about Quaternionic Möbius Transformations and Relativistic Kinematics. Some Python Scripts for numerical verification. Disclaimer: This document is a "Working Paper" and represents a research-in-progress draft (January 2026). It includes technical notes and a truncated version of a forthcoming monograph. While the mathematical core is verified, some sections of the 109-page draft may contain placeholders, temporary notes, or references to be finalized. It is published in Open Access primarily to establish chronological priority on the specific quaternionic and biquaternionic formulations described herein.