Four linear theories are considered in this chapter. Each has a distinctive and interesting history. Each one of the theories was originally formulated between 1820 and 1860. Representative of the theme of this chapter are the opening lines of the Historical Introduction in A.E.H. Love’s Theory of Elasticity (original edition, 1892):​ “The Mathematical Theory of Elasticity is occupied with an attempt to reduce to calculation] the state of strain, or relative displacement, within a solid... object... which is subject to the action of an equilibrating system of forces, or is in a state of slight internal relative motion, and with endeavours to obtain results which shall be practically important in applications to architecture, engineering, and all other useful arts in which the material of construction is solid.”