The Babington Plot was a Catholic plot in 1586 to assassinate Queen Elizabeth, a Protestant, and put Mary, Queen of Scots, a Catholic, on the English throne. It led to the execution of Mary. The long-term goal was an invasion by the Spanish forces of King Philip II and the Catholic League in France, leading to the restoration of the Catholic religion in England. The chief conspirator was Sir Anthony Babington (1561–1586), a young Catholic nobleman. The leading Catholics in England were loyal to Elizabeth and rebuffed overtures to support the plot. The actual designers were Don Bernardino de Mendoza in Paris and King Philip II in Madrid.
Much use was made of ciphers, which were intercepted on the orders of Francis Walsingham, who made use of Thomas Phelippes, a cipher and language expert in his employ.
More information on the Wikipedia page [1], which has links to articles on the several participants.
The National Archives Page is [2].