In many neurophysiological studies and brain-inspired computation paradigms, there is still a need for new spike train analysis and learning algorithms because current methods tend to be limited in terms of the tools they provide and are not easily extended. This chapter presents a general framework to develop spike train machine learning methods by defining inner product operators for spike trains. They build on the mathematical theory of reproducing kernel Hilbert spaces (RKHS) and kernel methods, allowing a multitude of analysis and learning algorithms to be easily developed. The inner products utilize functional representations of spike trains, which we motivate from two perspectives: as a biological-modeling problem, and as a statistical description. The biological-modeling approach highlights the potential biological mechanisms taking place at the neuron level and that are quantified by the inner product. On the other hand, by interpreting the representation from a statistical perspective, one relates to other work in the literature. Moreover, the statistical description characterizes which information can be detected by the spike train inner product. The applications of the given inner products for development of machine learning methods are demonstrated in two