The Order of the Garter is a secular company, a reincarnation of knights of the "Round-Table", dedicated to St. George the dragon slayer of the late 200's in the Byzantian Empire and subsequently adopted by the crusaders. Others see St. George as being part of Edward III's propaganda machine, St. George replacing Edward the Confessor as the Patron Saint of England and St. Michael the dragon slayer. Edward III successfully established St.George who became to be reguarded as the patron of knights all over Christendom.
The first 'Round-Table' gathering was held in 1344 at Windsor. Between October 1347 and the end of 1348,  following the incredible successes in France, tournaments were held including those at Windsor. Either on the 10th or the 24th of June 1348 the first Garter Ceremony was held in St. George's Chapel.. The idea for the Garter came to Edward III at the conclusion to a Windsor tournament in 1344.³
The opportunity arose from a mishap at a ball probably held at Calais after the fall of that city to Edward's siege in 1347. The concept embraced the establishment of a new Camelot around a table of Edward's closest knights.³ See St. George as depicted in the 1300's 

On the 10th August 1348, whilst the plague swept through England, the founder knights filed  in pairs into St. George's Chapel for their first investiture. The lines parted thence to seat themselves behind either the king or the Black Prince. They faced each other across the chapel like the opposing tournament teams they were meant to represent.
The previous 15 years of Edward III's reign had been so militarily successful that it was seen that only with God's help such achievements could have been made [Halidon, Neville's Cross, Crecy, Calais, Potiers] but essentially the investiture remained a non-religious occasion. 
The formation of the Garter Knights who emulated the fabled knights of King Arthur was in part Edward III's way of bringing together the descendants of the warring parties of his father's less than successful reign. By claiming the high ground in an idealogical chivalric code, Edward managed to develop the courtly and knightly behaviour which became a part of  a gentlemen's behaviour at court which gradually spread, by imitative fashion, to the general population. Prior to this, knights had lived principally by the sword under a feudal sytem which promoted itself in a never ending bout of revenge between knightly families and between the nobles and the kings. A certain kind of behaviour was expected of the 'new age' knight, an ideology based upon a group of knights in a medieval romance, Morte D' Arthur.
In the 1190's Hugh De Morville of  Cumberland & Westmorland is said to have taken the local story of Arthur in written form to the Continent when he replaced King Richard of England as a hostage of the Austrians. This work influenced Ulrich Von Zatzighoven who in turn influenced Chretien De Troyes  who wrote Morte D' Arthur which reintroduced Arthur into Britain as a medieval French romance.

A copy of the Winchester table made for King Edward I that was repainted during Henry VIII's reign

They filed into St. George's Chapel, Windsor Castle on the 10th August 1348 in pairs, the lines parting to seat themselves behind either the king or the Black Prince. They faced each other across the chapel like the opposing tournament teams they represented.

When each Garter Knight was created they were given a brass and enamel stall plate which was affixed to their stall in the chapel. They entered the chapel in 13 pairs which is probably the number of men in a jousting team.
When a knight companion was created, besides the stall plate, a crested helm and banner were displayed there. On the Garter knight's death the banner and helm were taken away but the stall plate remained.
A knight who was attainted was degraded from the Order. For example the 4th Duke of Norfolk who entered the Order in 1559 tried to dethrone Elizabeth I, for this treasonable act he was attainted and executed. The stall plate was removed in 1572 and not replaced until 1955. [an earlier Duke of Norfolk's daughter had married the 6th earl Warenne and so quartered the Warenne arms on his own].

Today, the Trooping of the Colour and the investiture of The Knights of the Garter are performed on the Queen's Official birthday, the second Saturday in June. This was chosen as Queen Elizabeth II's birthday in April falls at a time of unreliable weather.
 

After 1347, following Crecy, Edward founded the "Order of the Knights of the Blue Garter" consisting of himself and 26 of his most renowned companions. The Order was housed in the original St. George's Chapel part of Windsor Castle. St. George's Chapel was rebuilt in 1475 under Edward IV. One of the earliest burials here in the renewed chapel was Henry Holland , 3rd Duke of Exeter who was married to Anne, Edward IV's sister. Holland was the only legitimate male descendant of  John of Gaunt and the House of Lancaster until he was found dead in the English Channel in September 1475. His burial at the chapel was despite the fact that in his later years he had divorced Anne and joined the Yorkists.

Garter Stall Plate of Sir Thomas Beauchamp

King Edward III created the Order of The Garter for his bravest knights. The Order won its name and motto when according to Froissart the 'Countess of Salisbury', his possible mistress, dropped a garter at the ball  about 1347-1348. He boldly picked it up and fastened it to his own leg and to counter the sniggers, and declared: "Honi Soit Qui Mal Y Pense" loosely translated to "Shame on him who thinks evil of it".
Indicating the humour of Edward III, the Order of the Blue Garter was born and the motto remains on the coat of Arms of the Royal Family to this day. This act by the king is speculated to be a counter to the perception by the assembled guests that the king was having an affair with 'the Countess of Salisbury' such that he made light of it by turning the embarrassment around and making it an honour for the Court was aware of the king's love for the countess³ Personally I think, Edward being the paramount of chivalry [at least popularly] was trying to salvage a ladies honour. Edward III is supposed to have raped and battered the "Countess of Salisbury", perhaps at Nottingham. But this was possibly a piece of French propaganda from the Hainault chronicler Jean le Bel written in an attempt to cast a sleight upon the King of England, for le Bel's narrative is full of errors when compared  other sources. The assembled guests no doubt relished the symbolic embarrasment of the slipped garter. The Regent thereafter had to kneel and affix the Garter to the honoured knight's leg at the Garter ceremony in St. George's Chapel, Windsor Castle.

Froissart says of the alleged affair:

The Italian Polydore Vergil's twenty-six volumes of Anglicae Historicae Libri, written over a hundred and fifty years later, first claimed that it was Joan of Kent who was the 'Countess of Salisbury' and that she prompted the garter incident. Later researchers suggest that it was Joan's mother-in-law, Katherine Grandisson who was widowed by 1344 after William her husband and the first earl died.

UPDATE: A thorough search of the C.P.R. indicates that Joan was never referred to as the  'Countess of Salisbury'! 'Joan of Kent' does not appear, as we would expect her salutation to be, as 'Joan, wife of William de Monte Acuto, earl of Salisbury'. The reason for this is that the man she married in 1341, who became William Montacute 2nd earl of Salisbury, did not come of age until 1349. In the C.P.R. he does not appear as the earl of Salisbury until 1350. Gransden states that he did not receive livery of his lands until 1349⁷. Before 1350 he is merely referred to as the 'heir of William de Monte Acuto earl of Salisbury' and the ward of  Edward III. Similarly Joan is referred to as the 'wife of William de Monte Acuto, son on William de Monte Acuto, earl of Salisbury'. The Pope granted a marriage annulment to Joan and William in 1349 when they were both aged twenty / twenty-one which seems to have coincided with William becoming the 2nd earl of Salisbury.

Froissart's successors mistakenly used the title 'Countess of Salisbury' at the Garter Ball to mean Joan, and thus the Garter incident seems to have originated with the widow of the first earl of Salisbury's wife, Katherine Grandisson not Joan of Kent. Katherine's husband, the first earl, died in 1344 and Katherine was thus widowed from the age of about 40 [1344] to age 45 [d. 1349] which encompasses the time of a possible ball held after the Siege of Calais [which lasted from Sept. 1346 to August 1347] or shortly thereafter, for the Garter ceremony was inaugurated between October 1347 and the end of 1348.

Joan of Kent about 1352 was styled 'Countess of Kent', after her brother John died in that year. Like Katherine she may have been wooed but unlike Katherine, not won by the king, for she was in love with the earl of Salisbury's steward, Thomas Holland, to whom she had secretly been promised and then married in the sight of witnesses at age twelve [1340]. Either to be closer to her lover or for fear that Thomas would be executed when he returned from France, Joan did not divulge her first marriage at her second marriage to William II Montacute in 1341. Eventually, Thomas Holland returned to England and after beseeching King Edward and the Pope he received an annulment, through a Papal Bull, of Joan's marriage to William Montacute. Thomas and Joan had four children but after Thomas' death in Normandy in 1360, Joan clandestinely married Prince Edward the 'Black Prince'. 
Thus successive chroniclers have conflated the title 'Countess of Salisbury' with Joan of Kent,  Katherine de Montacute [Grandisson] ans even Alys [Alice] Montacute, wife of Edward Montacute the brother of the1st earl. We now need to make a sharp distinction between Joan of Kent and Katherine Grandisson who after her husband's death was the dowager countess of Salisbury. Katherine was the countess whom King Edward was infatuated with [whether the rape occurred or not] and she was the same person who lost the garter. Joan of Kent was not the countess of Salisbury

A drawing of  a garter  or stall-plate for Sir Thomas Banastre showing argent a  cross patonce sable.

St George's Day is celebrated on the 23rd of April each year. At this time St. George's flag is flown from every Christian Church in England. However, most people are not aware that before almost mythical St. George became the patron saint of England, the English king, Edward the Confessor had been its principal patron.

Edward III's friend
Sir Thomas de Beauchamp 3rd earl of Warwick was a knight of the Garter, a friend to Edward III and a guardian of the boy king, Richard II. The Arms of the earl of Warwick included an heraldic bear which is incorporated today into the Arms of the town of Warwick. A brass of Sir Thomas Beauchamp and his wife, Margaret appears in St. Mary's Church, Warwick dated to 1406.
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Link : Artorius- Leader of the Roman Britons.