From Wiki:

A deed of 1369, now in the possession of Eton College, refers to the “gildaule”, and a charter of 1439 states that “pleas happening in the said borough … shall be pleaded and holden in the guildhall there, before the mayor and bailiffs for the time being”.^[2] Norden’s map of 1607 shows a market house in the location of the present guildhall: the main part of it is raised on wooden pillars to allow the space beneath to be used as a covered corn market.^[3]

The erection of the present guildhall was begun in 1687, under the direction of Sir Thomas Fitz (Fitch or Fiddes) but the story is that on his death in 1689, the task was taken over and completed by Sir Christopher Wren. The cost of construction was £2687/1s/6d. The new building was supported by stone columns, like its predecessor. This allowed for corn markets to be held in the covered area.^[2]

Windsor Guildhall is home the the Windsor & Royal Borough Museum. The Museum tells the story of the Royal Borough of Windsor & Maidenhead and has over 100 objects on display ranging from the Stone age to the present day.

Windsor Guildhall, is a historic Grade I listed building with important portraits of the Royal Family from Elizabeth I to Elizabeth II. It was designed by Sir Thomas Fitch and buils in 1689. Fitch died before its completion which Sir Christopher Wren may have overseen. An extension was added in 1829 which was designed by Sir James Bedborough, Mayor of Windsor.*

*Information from a signboard next to the museum