Functional-differential equations with affine modification of the argument have been intensively studied due to their multitude of applications in physics, biology or economics. The book opens with a chapter on basic notions in metric spaces and fixed point theorems, followed by a general survey of various types of functional-differential equations. The Cauchy problem for the equation \[ y'(x)=f(x,y(x),y(\lambda x),y(x-\omega)) \] with affine modification of the argument, and some of its generalizations, is studied in Chapter 3, with accent on existence and uniqueness theorems, and the dependence on initial values. The next chapter contains boundary value problems \[ z''(x)=F(x,z(x),z(\lambda x)),\quad x\in [0,b],\;0<\lambda <1, \qquad z(0)=\alpha ,\;z(b)=\beta, \] and related types. Analytical and approximate solutions to some equations with linear modification are studied in Chapters 5 and 6, respectively. The book is self-contained and can be useful to students with a background in differential equations and to researchers in this field (the bibliography contains 140 titles).