The presentation contained in what follows provides extensive coverage of linearly constrained linear models. The format is one in which the results are regarded as constituting the initial section of an initial chapter in a treatise that adds to the coverage of linear models provided by the seven chapters of the book Linear Models and the Relevant Distributions and Matrix Algebra. Accordingly, the results are envisioned as forming Section 1 of a Chapter 8, and are so regarded for such purposes as the numbering of equations and in making references and citations. Some additional references are listed at the end.