This chapter is intended to give a brief introduction as well as a summary of the present text. We shall highlight some of the main ideas and methods behind the theory and will also aim to provide some background on the main concept in the manuscript: the notion of so-called (formula presented) dating back to Picard in the seminal paper (Picard, Math. Methods Appl. Sci. 32, 1768–1803 (2009)); see also (Picard and McGhee, Partial differential equations: A unified Hilbert space approach, Chapter 6, vol. 55. Expositions in Mathematics (DeGruyter, Berlin, 2011)).