Over the past two decades, the “explosion” of quantitative and mathematical research in slope geomorphology has been particularly striking, giving rise to intense debate and discussion. All of these debates revolved around a single question: What can mathematics contribute to geomorphology? Numerous arguments were advanced both in support of and against its application, yet no consensus emerged. Now that the controversy has largely subsided, the time has come to reflect calmly on the advantages and disadvantages of using mathematical methods in geomorphology. There is no need to enumerate all the studies that have employed such methods, as they are both numerous and highly diverse. One major drawback of these approaches is the absence of a common conceptual basis and an overarching framework capable of integrating individual studies into a rigorous scientific theory. The formation of such a theory has been hindered by a particular circumstance. On the one hand, the aforementioned “explosion” attracted the attention of a large number of researchers; on the other hand, it led to such diversity in methods and research results within slope geomorphology that they could not be unified into a single direction, either theoretically or practically. Consequently, the accumulation of facts did not result in the creation of a unified theory. Although this situation is discouraging in itself, its positive aspect is that, within this diversity, one can clearly identify a number of studies whose systematization may contribute to the further development of a unified theory of geomorphology, a theory grounded in the substantive analysis of theoretical propositions, experimental data, and field observations. During the past ten to fifteen years, we have developed and published a large number of mathematical models describing different types of slopes, slope-forming processes, and the development of other landforms. A wide variety of mathematical tools have been employed for this purpose. The problem is that not all mathematical methods are truly suitable for describing the development of particular types of slopes and their associated processes. It has become evident that each type of slope can be described only through specific mathematical approaches appropriate to its development. This led us to propose the idea of a unified theory for describing slope evolution, in which each initial slope type corresponds to its own family of slope-system models. Our research experience indicates that, in slope geomorphology, it is necessary to distinguish between a general theory of deterministic equilibrium models (developed separately for one-dimensional, or planar, and two-dimensional, or spatial, problems) and a new field that we have established: dynamic models of slope systems based on the qualitative theory of dynamical systems. These models describe the processes of interaction among the various elements of slope systems and the factors acting upon them. The problem of interaction is ubiquitous in geomorphology, and the interaction among components of a slope system plays a decisive role in describing slope development. Unlike equilibrium-model concepts, dynamic models do not directly describe the evolution of slope profiles and their spatial forms; rather, they investigate the physical essence of the processes involved and construct a theory of development. Thus, the theory of geomorphic dynamic equilibrium is represented through the concept of dynamic models. In addition, there exists a class of problems concerned with boundary conditions, which must be specified in order to solve problems related to particular types of slopes. The third part of this book, devoted to slope processes, may appear somewhat unusual, as these processes might seem to precede the description of landforms themselves. In fact, according to our conception, this section is intended to serve as an illustration of the practical application of mathematical methods in slope geomorphology. Since current applications remain selective, the third part is necessarily fragmentary in character as well. In the first two parts, slopes are considered both as closed systems and as open systems; subsequently, however, boundary modeling will be introduced, including boundaries associated with hydrological systems and other related systems. Owing to limitations of space, methods for solving boundary-value problems are presented only for non-standard cases. The author expresses sincere gratitude to Professor D. G. Simonov, Associate Professor O. A. Bolsuk, and I. M. Zeidis, Head of the Mathematical Modeling Laboratory of the Department of Geomorphology at Moscow University, for their valuable comments and suggestions during the review of this manuscript. The author also extends heartfelt thanks to Professor A. V. Stupishin, the scientific editor of this volume.