Kant served as dean of the philosophy faculty six times, and twice as rector of the university (see accounts of his service; and on the particular duties of the dean, rector, and academic senate, see the page on university governance and regulation.) As noted there, the offices of faculty dean and rector rotated each semester among the releveant faculty; the installation of the new rector was called a Rektorwahl, which suggests that candidates were elected into office, but that was not the case.
Despite the additional duties that came with these offices, Kant continued to teach the same number of courses during those semesters when he served as rector or as dean, as can easily be seen from the table of his lecturing activity (indications of his office are given in the left-most column, with the semester).
Kant became eligible to serve as dean once he was a full professor, and the position rotated every semester among the eight professors in the philosophy faculty. One might therefore think that Kant would serve as dean sometime within the first eight semesters, and then every eight semesters thereafter. Instead, he first served as dean in his 13th semester (SS 1776), and then in his 20th, 26th, 32th, 36th, and 43th semesters. Kant’s 7th turn as dean came again WS 1794/95, but Kant was wanting to devote his time to his writings, so J. C. Kraus filled in for him, and his 8th turn (SS 98) was filled in by Mangelsdorff, as was his 9th turn in WS 1801/02 [Reicke 1860, 52], concerning which we have the following letter from Professor Wald, writing as dean on behalf of the philosophy faculty (30 July 1801):
Out of respect for your many years of service at our academy and out of collegial friendship, we have resolved to entirely excuse you from your term as dean, according to your wish, and that you will retain your previous share of the faculty incomes, as well as interests in matriculation fees. The dean’s honorarium will instead go to whomever’s turn it is to serve as dean. We hope you find this wholly in accordance with your thoughts on the matter.... [AA 12:440-41]
 According to a decree of 25 May 1719 one assumed the dean’s office in the philosophy faculty only after one’s second time through the rotation this was presumably to ensure that one had served as a full professor for at least eight semesters before being asked to serve as dean. Kant’s first term as dean came in his thirteenth semester as a full professor. The decree is reprinted in Arnoldt [1746, ii.77-78, appendix #55].
 On Kant’s duties as dean, and in particular the need to examine incoming students, see the relevant discussion under Students: Student Life on entrance exams. See also Dietzsch [2003, 123-30].
Kant entered the senate after Christiani’s unexpected death on June 21, 1780. Dietzsch [2003, 131] quotes from a declaration from the East Prussian government to the university (11 Aug 1780):
We want hereby to confer and confirm the improvement for the very deserving Professor of Logic and Metaphysics Kant the vacated position in the academic senate, with the attached salary of 27 Thr. 75 gr. 10 Pf.
Wir wollen dem jede Verbesserung so sehr verdienenden Prof. Log. & Met. Kant die vacant gewordene Stelle im academisch. Senat mit den dabey aufkommenden Emolumenten a. 27 Thr. 75 gr. 10 Pf. hiemit conferiren und darin bestätigen.
The other senators were W. B. Jester and C. R. Braun (Law), J. C. Bohl and A. J. Orlovius (Medicine), T. C. Lilienthal and G. C. Reccard (Theology), and in philosophy J. S. Bock (Greek), J. F. Werner (rhetoric), and F. J. Buck (mathematics). Buck would have entered the senate just a year previously, in 1779, upon the death of G. D. Kypke. Werner would die in 1782, Bock in 1785, and then Buck in 1786, quickly making Kant the senior philosophy professor, surrounded by two former students (C. D. Reusch would replace Werner, Christian Kraus would replace Bock), and the recently arrived Mangelsdorff (replacing Buck). Kant's retirement from the senate was surrounded by some controversy (see the discussion of Kant's retirement), and Kant eventually agreed to cede his position in a letter of November 14, 1801.
Serving on the senate carried a small annual stipend (27 rth., 75 gr. 10 pf.) and allowed Kant to provide free meals for an amanuensis at the Alumnat [glossary], but it also obliged Kant to attend the weekly senate meetings each Wednesday, and made him eligible to serve as rector of the university, roughly every eight years (the professors in the upper faculties normally served as rector every four years).
 The senate met each Wednesday at either 9 or 10 in the morning. Each of these times are given as a standard time; Stark suggests they might vary between summer and winter semesters [1993, 226].
Kant’s first term as rector came in SS 1786, the Rektorwahl [glossary] falling on Sunday, 23 April 1786, a day after his 62nd birthday. Kant dressed in a black suit of clothes purchased for the occasion, black being the required color, but one normally not found in his wardrobe [Jachmann 1912, 167, repr. in Malter 1990, 297]. The Rektorwahl this semester was especially memorable, since a deranged medical student forced his way to the lectern during the ceremony and tried to announce his lectures for the coming semester. Rink reports:
The outgoing prorector, the late Doctor and Professor Holtzhauer, gave his retirement speech, and Kant had just begun his inaugural speech, when a mentally deranged former student quickly pushed his way through the audience, stood next to Kant on the high lectern of the large academic lecture hall, pulled out a paper, and began to announce his lectures. He was quickly removed from the premises by an overwhelming number of hands. [Rink 1805, 49-50; repr. in Malter 1990, 298]
Kant’s second term as rector was SS 1788, and his third in SS 1796. This was Kant’s last semester to hold lectures, and he passed up the rectorship to Reusch, as well as the monetary benefits (amounting to over 150 rthl.) attached to the rectorate [Kraus, in Reicke 1860, 53].
 Apparently Kant’s choice as rector was not straight-forward, as Hamann related in a letter the week prior to the festivity (March 26 letter to F. H. Jacobi):
Kant will become Rector magnificus for the first time, and the ceremony occurs on Quasimodogeniti Sunday, the day after his birthday. There were many difficulties with the choice, which Kraus explicated and lifted with a masterful deduction, which I came to read without his knowledge. Kant conducted himself in a most noble and philosophical manner that honored his good character, which none can deny him. He is now working on a new edition of his Critique...
Kant wird zum ersten male Rector magnificus, und der Actus geschieht am Sonntag Quasimodogeniti, den Tag nach seinem Geburtstage. Bey seiner Wahl sind viele Schwierigkeiten gewesen, die Kraus durch eine meisterhafte Deduction erläutert und gehoben, welche ich ohne sein Wissen zu lesen bekommen. Kant hat sich auf eine sehr edle philosophische Art dabey betragen, die seinem guten Charakter, den ihm niemand absprechen kann, Ehre macht. Er arbeitet jetzt an einer neuen Auflage seiner Critik.... [Jacobi 1812-25, vol. 4.3, p. 188; also printed at Hamann 1955-79, vi.361]
‘Quasimodogeniti’ [Latin: “as newborn babes”] is the name for the Sunday following Easter Sunday. 'Deduktion' is meant here much as Kant used it in his Critique (e.g., the transcendental deduction), namely, in the sense of a “legal deduction,” whereby the legitimacy of a legal claim, such as a claim on a piece of land, is established by tracing the claim back to its origin.
 Kant’s Latin address is no longer extant, unless it is his “On Philosophers’ Medicine of the Body” [writings], which Adickes believed was his retirement speech after his second term as rector in 1788. Kant’s colleague Johann Schultz [bio] claimed that the only academic speeches that Kant gave were at the end of his rectorate [Reicke 1860, 38].