To get an impression of the contents of nonlinear Perron–Frobenius theory, it is useful to first recall the basics of classical Perron–Frobenius theory. Classical Perron–Frobenius theory concerns nonnegative matrices, their eigenvalues and corresponding eigenvectors. The fundamental theorems of this classical theory were discovered at the beginning of the twentieth century by Perron [179, 180], who investigated eigenvalues and eigenvectors of matrices with strictly positive entries, and by Frobenius [70–72], who extended Perron's results to irreducible nonnegative matrices. In the first section we discuss the theorems of Perron and Frobenius and some of their generalizations to linear maps that leave a cone in a finite-dimensional vector space invariant. The proofs of these classical results can be found in many books on matrix analysis, e.g., [15, 22, 73, 148, 202]. Nevertheless, in Appendix B we prove some of them once more using a combination of analytic, geometric, and algebraic methods. The geometric methods originate from work of Alexandroff and Hopf [8], Birkhoff [25], Kreĭn and Rutman [117], and Samelson [192] and underpin much of nonlinear Perron–Frobenius theory. Readers who are not familiar with these methods might prefer to first read Chapters 1 and 2 and Appendix B. Besides recalling the classical Perron–Frobenius theorems, we use this chapter to introduce some basic concepts and terminology that will be used throughout the exposition, and provide some motivating examples of classes of nonlinear maps to which the theory applies.