Quum cum subjūnctīvō
Quum with the subjunctive

quum narrativum vel historicum  “when”;  when describing temporal circumstances and the subject of main and subordinate clauses is the same, the imperfect or pluperfect subjunctive is used:  “with/as/after … -ing”

When something is narrated, and the subordinate clause is introduced by the conjunction quum, it makes that clause a temporal one, which takes the subjunctive.  Thus :

« Quum hæc dixisset (When he had said these things),… » ;
« Quum morbo et senectute premeretur  (When he was weighed down by sickness and old age),… ».

And the inscription in Rome on the famous obelisk of the ancient sports arena reads:

« Obeliscum ab Imperatore Caracalla Romam advectum, quum inter circi castrensis rudera confractus diu jacuisset, Innocentius Decimus Pont[ifex] Opt[imus] Max[imus] ad fontis foriq. ornatum transtulit, instauravit, erexit anno salutis MDCLII Pontif[icatus sui]. VII. »
“[This] obelisk, brought to Rome by Emperor Caracalla, while it had long lain broken amidst the rubble of a military sports stadium, Innocentius the Tenth, the Great and Good Pontiff, transported ornamented to [this] fountain and plaza, [and] restored and set it up in the Year of Salvation 1652, the 7th year of his Pontificate.”

« Quum meridies appropinquaret, dux exercitum in castra reduxit. »  “As noon approached, the leader drew the army back into camp.”
« Quum Cæsar ad oppidum accessisset, cives a Romanis pacem petierunt. »  “After Caesar had come up to the town, the citizens besought the Romans for peace.”
« Quum tætra prodigia nuntiata essent, decemviri Sibyllinos libros adī jussi sunt. »  “After foreboding omens had been announced, the decemviri were ordered to consult the Sibylline books.”
« Quum a me quoque id responsum tulisses, … ad Quintum Metellum prætorem venisti. »  “After having received that answer from me …, you went to the prætor, Quintus Metellus.”  (Cicero, Catiline, I, 19.)

quum causale  “since ;  given that ;  whereas” ;  often quippe quum “especially since” ;  præsertim quum “especially (since, seeing that, when)”

When the statement indicates a cause by which something happens, the subjunctive is required.  Thus :

« Hædui, quum se suaque ab Helvetiis defendere non possent, legatos ad Cæsarem mittunt. »
“The Haeduans, since they could not defend themselves from the Helvetians, send envoys to Caesar”  (Cæsar, De Bello Gallico, I, 11, 2.)
« Quæ quum ita sint, … »  “Since these things are so, …”.
« Quum vita sine amicis tristis sit, ratio nos admonet ut amicitias comparemus. »  “Since life without friends is sad, reason itself admonishes us to create friendships.”

quum concessivum  “though, although, in spite of the fact that”

When there is a concession which concedes but undermines what is affirmed in the next clause, the subjunctive is required:

« Socrates, quum facile posset educi e custodia, noluit. »  “Socrates, although he could have easily been released from imprisonment, did not want it.”  (Cicero, Tusculanæ Disputationes, I, 29, 71.)
« Quum plurima possideant, plura petunt. »   Although they possess many things, they seek more.
« Fuit pauper, quum dives esse posset. »  “He was poor, in spite of the fact that he could have been rich.”

In these sentences, quum concessivi can be replaced by etsi or quanquam with the indicativo ;  or by quamvis or licet, with the subjunctive ;  or even, finally, by etiamsi with the indicative or the subjunctive.

quum adversativum  “whereas”

In addition, the subjunctive mood is used in an adversative secondary clause :

Socratis ingenium variosque sermones immortalitati scriptis suis Plato tradidit, quum ipse Socrates nullam litteram reliquisset.  (Cicero, Orator, III, 16, 60.)
In his writings, Plato transmitted to immortality the brilliance and various speeches of Socrates, even though Socrates himself had left no writings.

« Numerus equitum nostrorum erat quinque milia, quum hostes non amplius octingentos equites haberent. »
“The number of our cavalrymen was five thousand, while the enemy did not have more than eight hundred horsemen.”

« Otiosus quum sis, te dicis esse sedulum. »
Although you are at leisure, you say you are busy.

« Solus homo particeps est rationis, quum cetera omnia animalia expertia sint. »
“Only man is gifted with reason, whereas all other creatures are devoid of it.”

Quum cum indicativo
Quum with the indicative

quum temporale  “when, at the time when;  at the same time that”

When only the time of an action is indicated, the indicative is required :

« Quum eris me assecutus, coram agemus quæ erunt agenda. »
“When you will get to my place, we will deal in person with what has to be done.”   (Cicero, Ad Att., III, 5, 1.) ;

« Quum vēneris, cognosces. »
“After you will have come, you will understand.”  (Cicero, Ad Att., I, 3, 4.)

« Quum Cæsar in Galliam vēnit, alterius factionis principes erat Hædui, alterius Sequani. »
“When Caesar came to Gaul, the leaders of the one side were the Haeduans, of the other, the Sequanians.”

« Tum quum copiæ Persarum ad Platæas victæ sunt, simul in Asia dimicatum est. »
“At the same time when the forces of the Persians were defeated at Plateae, a battle occurred in Asia”

« eo tempore quum »  “at the time when”
« eo die quum »  “on the day when”

« Eo tempore paruisti quum necesse erat. »
“You appeared at the time when it was needed.”

quum iterativum  “whenever, as often as, every time that”  (occasionally with the subjunctive) signifies an action of the same or prior time :

« Quum cohors impetum fecerat, hostes velocissime refugiebant. »
“Whenever the cohort had made an attack, the enemy would flee very quickly.”

« Quum rus ivi, otium me delectat. »
“Whenever I went to the country, the leisure delights me.”

« Græci oracula consulebant quum bella erant inituri . »
“The Greeks would consult oracles whenever they were about to go into wars.”

« Verres, quum rosam videbat, tum ver incipere arbitrabatur. » 
“Whenever Verres would see a rose, he would think spring was beginning.”

quum inversivum vel additivum  “when (suddenly)”

When a compound sentence contains a main past action in a secondary clause with quum, its verb is put in the indicative perfect.

« Vix exercitus Romanus extra munitiones processerat, quum Galli flumen transierunt. »
“The Roman army had hardly gotten outside of the fortifications when the Gauls crossed the river.”

« Milites jam muros urbis ascendebant, quum repente hostes eruptionem fecerunt. »
“The soldiers were already climbing the walls of the city, when the enemy suddenly made an unexpected attack.”

« Cenabam quum redditæ sunt tuæ litteræ. »
“I was in the midst of eating dinner when your letter was delivered.”

quum explicativum or coincidens (or “identicum”)  “by …-ing, when, while, because ;  in the case where ;  through the action of”

Always with the indicative, and both clauses have the same tense.

« Quum hoc confiteris, scelus te admisisse concedis. » 
“In confessing that, you admit to having committed a crime.”

« Quum taces, facinus confiteri videris. »
“By keeping silent, you seem to be confessing to the crime.”

« Quum quiescunt, probant. »
“By staying quiet, they are approving it.”

« Quum tacent, clamant. »
“In staying silent, they are crying out.”