Edward IV was king during the Wars of the Roses. As the son of Richard, 3rd Duke of York, he inherited his father's claim and after the battle of Townton he was crowned King of England . Edward loved hunting, feasting, drinking and womanising, was very tall and in later life became more inactive and fat, which may have lead to his death.
But today we're only slightly interested in that. What we want to know about is his hats.
As we can see he has a fairly simple black velvet cap with an elaborate decoration - probably embroidered, but it could be jewelry. Although not perfectly clear, the decoration seems to be based on a coat of arms or seal.
On this Edward IV groat from his second reign we can see him wearing a crown. The depiction is not clear enough to say a lot about it, but it seems to be a circlet with fleur-de-lis sticking up from it. Also his hair is quite a bit wilder!
Edward was a noted general and warrior. The Wars of the Roses are traditionally considered Late Medieval. Armour reached it's high point during this period, as it developed to protect wearers from crossbows, longbows and early firearms. The high quality of the armour allowed the wearer to fight without a shield, and, indeed, penetrating armour from this time with single handed weapons is extremely difficult. Edward would have worn a Sallet (depicted above) the helmet of choice for all professional soldiers of 15th century Western Europe.
More royal hats every day until the royal wedding.
 Lancastrians preferred to continue to uphold Henry VI claim leading to Edward IV having to flee the country in 1470, only to return and reclaim the throne in 1471.
 Which lead directly to the illegitimacy of his sons. Viewers (and readers) of Game of Thrones may be interested to know that Edward IV was a major inspiration for the character King Robert Baratheon.
 Some historians date the end of the medieval era in England to the death of Richard III.