This chapter provides an introduction to stability properties for the family of solutions to dynamic systems. Since nonlinear differential equations mostly govern the evolution of observed economic phenomena, the chapter begins with focusing on the family of solutions for the state variable in one-dimensional, first-order, nonlinear autonomous dynamic system. The one-dimensional systems give the possibility to illustrate the various stability properties and rapidity of motion (growth) with explicit solutions of the single dynamic (differential) equation. Besides the traditional concept of asymptotic stability, new stability criteria—strong/weak absolute, strong/weak relative, strong/weak logarithmic stability—are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.