This book sets forth the authors' Neo-Newtonian mechanics with extension to relativistic velocities but without recourse to Einstein's relativity theories. It is motivated by Eric Laithwaite's infamous lecture to the Royal Society that (more or less) resulted in him being run out of town on a rail. The authors have set themselves the task of giving a rigorous and elementary theory to explain his amazing demonstrations, but using only as minimal a modification of Newtonian mechanics as both possible and necessary so that this derivation can be considered to be algorithmic in nature with the...