Framed by the previous largely theoretical ones, this chapter looks at contemporary developments in law and administration from several angles. There is a pervasive sense of change, most obviously associated with, but not confined to, the extended Brexit process.

It is fair to say that international law has always considered its fundamental purpose to be the maintenance of international peace. Although ethical preoccupations stimulated its development and inform its growth, international law has historically been regarded by the international community primarily as a means to ensure the establishment and preservation of world peace and security. This chapter is concerned with the procedures available within the international order for the peaceful resolution of disputes and conflicts, except for judicial procedures covered elsewhere.

In this chapter we review probability and statistics. We define the ideas of probability, the probability density function, and the cumulative density function. We introduce Bayes’ theorem that relates prior, marginal, posterior, and conditional probability densities, which allows us to define the maximum a posterior and the maximum likelihood estimators. We discuss central moments of distributions. We review multivariate probability distributions including the correlated multivariate complex circularly symmetric Gaussian distributions. We also review a set of useful distributions, including Rayleigh, exponential, χ2, and Rician. Finally, we discuss random processes.

The rise of individual criminal responsibility directly under international law marks the coming together of elements of traditional international law with more modern approaches to human rights law and humanitarian law, and involves consideration of domestic as well as international enforcement mechanisms. Although the rights of individuals in international law have evolved significantly in the post-1945 era, the placing of obligations directly upon persons as opposed to states has a distinct, if narrow, pedigree. Those committing piracy or slave trading have long been regarded as guilty of crimes against international society bearing direct responsibility, for which they may be punished by international tribunals or by any state at all. Jurisdiction to hear the offence is not confined to, for example, the state on whose territory the act took place, or the national state of the offender or the victim. This universal jurisdiction over piracy constitutes a long-established principle of the world community. All states may both arrest and punish pirates, provided of course that they have been apprehended on the high seas or within the territory of the state concerned. The punishment of the offenders takes place whatever their nationality and wherever they happened to carry out their criminal activities.

The reader will probably be familiar with the notion of a real or complex vector space. In Galois theory we need to consider vector spaces over an arbitrary field 𝐾: we replace the field of scalars ℝ or ℂ by an arbitrary field 𝐾

The seas have historically performed two important functions: first, as a medium of communication; and, secondly, as a vast reservoir of resources, both living and non-living. Both of these functions have stimulated the development of legal rules. The fundamental principle governing the law of the sea is that ‘the land dominates the sea’ so that the land territorial situation constitutes the starting point for the determination of the maritime rights of a coastal state.