This monograph contains a detailed exposition of the up-to-date theory of separably injective
spaces: new and old results are put into perspective with concrete examples (such as l c0 and
C(K) spaces where K is a finite height compact space or an F-space ultrapowers of L spaces
and spaces of universal disposition). It is no exaggeration to say that the theory of separably
injective Banach spaces is strikingly different from that of injective spaces. For instance
separably injective Banach spaces are not necessarily isometric to or complemented subspaces
of spaces of continuous functions on a compact space. Moreover in contrast to the scarcity of
examples and general results concerning injective spaces we know of many different types of
separably injective spaces and there is a rich theory around them. The monograph is completed
with a preparatory chapter on injective spaces a chapter on higher cardinal versions of
separable injectivity and a lively discussion of open problems and further lines of research.
