Short answers, pulled from the story.
Matthias Corvinus was King of Hungary and Croatia from 1458 to 1490. He earned the epithet "the Just" from folk tales depicting him as a monarch who wandered his realm in disguise to deliver fair verdicts to ordinary people; the saying "Dead is Matthias, lost is justice" spread widely after his death in 1490.
Matthias Corvinus was proclaimed king on the 24th of January 1458 after his uncle Michael Szilágyi arrived at the Diet of Hungary in Pest with 15,000 troops and intimidated the assembled barons into a unanimous vote. His older brother had been executed in March 1457 and King Ladislaus the Posthumous died unexpectedly in November 1457, leaving the throne vacant.
The Bibliotheca Corviniana was the royal library of Matthias Corvinus and one of the largest book collections in Europe at the time of his death in 1490. Matthias began building it around 1465 under his first librarian Martius Galeotti from Ferrara; 216 volumes have survived, showing a preference for secular works including classical military treatises and histories.
The Black Army was a professional standing mercenary force that Matthias Corvinus began organizing around 1462, recruiting from the disbanded Czech mercenaries of John Jiskra. It was one of the earliest professional standing armies of medieval Europe and was used to conquer Vienna in 1485 and Lower Austria by 1487; after Matthias died in 1490, the unpaid army turned to plunder and was destroyed on the river Száva in 1492.
Matthias Corvinus made Hungary the first country outside Italy to embrace the Renaissance. He commissioned artists including Filippino Lippi, Andrea Mantegna, and Benedetto da Majano, rebuilt the palace at Visegrád in Renaissance style beginning around 1479, and in 1485 decided to commission Leonardo da Vinci to paint a Madonna. His marriage to Beatrice of Naples in 1476 deepened Italian cultural influence at his court.
Matthias Corvinus died on the 6th of April 1490 in Vienna. He participated in a Palm Sunday ceremony despite feeling ill, tasted a rotten fig, and lost consciousness the following day. Professor Frigyes Korányi concluded he died of a stroke; Dr. Herwig Egert did not exclude the possibility of poisoning. He was buried at Székesfehérvár Cathedral on 24 or the 25th of April 1490.