The following paper ”A unification scheme for classical and quantum mechanics at all velocities (I) Fundamental Formation of Material Particles” is a copy of the original manuscript first submitted to the Pro. Roy. Soc., February 24, 2003. Today, about two years after, we decide to publish it as is at the E-print server. Within the scheme for material particle formation and vacuum structure and dynamics presented in the paper, numerous new researches have since been carried out, including the Inference of Schrdinger Equation and the Prediction of Gravity. These results all re-affirm the viability of the scheme. Our augmented representation of this scheme as is today contains over 400 reprint pages and is published in two volumes of monograph in Refs. [3-4]. Within the topics treated in the original paper, there are also major supplements: (1) Systematic, detailed treatments of vacuum have been supplemented. Various discussions have been made much elaborately, or with better clarity. Some quantitative evaluations, esp. the vacuum density, are remade on more solid ground. (2) Some of the model entities are re-named. Especially ”a positive (oscillatory) elementary charge” is named an ”aether pole” in the original paper, and is renamed in later papers as ”vaculeon”, and a pair of two bound aether poles of opposite signs at ground state is renamed as a ”vacuuon”. (These changes for the better have benefited from discussions with Prof. R. Lundin.) The reader is hoped to find these updates and new contents in our recent papers [1-2], publications [3-4], and upcoming papers.