This book is about the Theory of Special Relatively (SR), the introductory parts of which, and other general comments on science and physics preceding it, would be of interest to the general reader. The alternative description of SR proposed and developed in the book is essentially that of Newton's classical physics, except for the critical additional of a step properly expressing the travel time of light signals conveying information to the observer. The form of that step, in turn, is dictated by the requirements of SR as expressed through its essence, the Lorentz transformation. Conventional interpretations of SR phenomena are as the observer perceives them, in altered descriptions of space and time. The altered versions differ from those associated with the phenomena at the location of the event creating them, because the light signals, conveying the information from source to observer, involve certain travel times of the signals themselves. Thus, until deciphered, they are not a simple representation of times in the event of interest. When the alternative approach to representation of SR developed in this book is applied, the same results as those from the conventional approaches of SR are obtained. The expressions for quantities such as energy and momentum differ from the corresponding quantities in Newton's model for space and time. The alternative approach in the book simply provides a more intuitive route to and a logical explanation of the relativistic process.