  This monograph offers an introduction to a collection of numerical algorithms
implemented in the library CodPy (an acronym that stands for the Curse Of
Dimensionality in PYthon), which has found widespread applications across
various areas, including machine learning, statistics, and computational
physics. We develop here a strategy based on the theory of reproducing kernel
Hilbert spaces (RKHS) and the theory of optimal transport. Initially designed
for mathematical finance, this library has since been enhanced and broadened to
be applicable to problems arising in engineering and industry. In order to
present the general principles and techniques employed in CodPy and its
applications, we have structured this monograph into two main parts. First of
all, we focus on the fundamental principles of kernel-based representations of
data and solutions, also that the presentation therein is supplemented with
illustrative examples only. Next, we discuss the application of these
principles to many classes of concrete problems, spanning from the numerical
approximation of partial differential equations to (supervised, unsupervised)
machine learning, extending to generative methods with a focus on stochastic
aspects.
