The Absolute State
In Kant’s day there were about forty universities in the German-speaking lands, and these were all quite small by today’s standards. Halle, the largest of them, enjoyed an enrollment of around 1000 students. Göttingen was the latest arrival, founded in 1736, and was also the fastest growing, with about 11-12% of the total student enrollment by 1775. The four largest German universities — Halle, Göttingen, Jena, and Leipzig — accounted for nearly half of the total student enrollment in Germany. This meant that some of the universities were vanishingly small (and as a result, many of them did indeed vanish). Königsberg, whose share of the students remained at about 5% throughout the 18th century (and growing slightly toward the end) had a student enrollment of about 370 when Kant began attending as a student, and enrollment oscillated between 250 and 380 during Kant’s years as a teacher (see the table on average enrollments here).
Four of these universities were Prussian: Halle, Königsberg, Frankfurt/Oder, and Duisburg. Königsberg had strong ties especially to Halle — for instance, in the early part of the century, all theology students were required to study for two years in Halle. Of those teaching in some capacity or other in the philosophy faculty at Königsberg during the 18th century for whom we have data (n=106), 17% studied, graduated, or had taught at Halle, another 17% at Jena; fewer came from Frankfurt/Oder, proportional to its smaller size; and 85% had either graduated from or studied at Königsberg — indeed, many of the faculty, like Kant, had grown up in Königsberg.
The set of highly abbreviated remarks on the fifty-two German-speaking universities that follow is somewhat haphazard and incomplete, based primarily on material provided in Eulenburg , Clark , and Ellwein . The purpose of this listing is to offer a rough and preliminary orientation to the community of German universities in which Kant and his associates were living and working. Additional information on student enrollment (All Universities, Königsberg) and staffing (Full Professors) is also available, as well as a modest list of 18th century professors at the different universities (and a few Gymnasia).
The founding year claimed for universities should be viewed with caution, as it was not always clear which event was used to determine the date (and as a result there are many inconsistencies to be found in the literature). The date might refer to when university privileges were granted; or to when classes were first held; or to when students could first matriculate; or to when the request for a charter was first made to the Holy Roman Emperor (or other secular authority) and to the Pope (or other ecclesiastical authority); or to when the public celebration of the founding took place. Similarly, many of these universities led lives as other kinds of schools prior to receiving charters as universities, and sometimes these earlier dates are given. In general, I follow Ellwein  on the dates.
With the chronological index, I follow the classification scheme and data in Ellwein [1997, 321-24]. Dates after 1800 (e.g., the re-founding of a university) have been omitted, and schools listed by Ellwein but not included here are: Lausanne (1537, theology; university since 1890), Molsheim (1618-1701), Anschaffenburg (1808-14), Passau (1773-1803, philosophy and theology), as well as the mining school at Freiberg (1765) and the art schools at Nürnberg (1662-4), Düsseldorf (1769-1805), and Dresden (1764).
 See, for instance, Walter Rüegg's discussion of the founding date for the University of Bologna: The date offered by the university — 1088 — would seem more closely tied to the need, in the late 19th century, to celebrate a significant jubilee and to support the unification of Italy, than to any identifiable event in the 11th century [1992, 4-6].