Summarize Chapters 1 and 2 of The Maltese Falcon.

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In Chapter 1, the book opens with the arrival of a beautiful female who calls herself "Miss Wonderly" entering the Spade & Archer Detective Agency. She wishes to have somebody called Floyd Thursby tailed by the detective agency. Miles Archer, who is a partner of this detective agency, quickly agrees to help Miss Wonderly, apparently more attracted by Miss Wonderly herself than the job she asks him to do, as he smiles at her in a lascivious fashion. 

In Chapter 2, the action truly begins when Sam Spade, the hardboiled detective protagonist of this novel, is woken up in the middle of the night with a phone call to tell him that Miles Archer has been shot dead. When he goes to the place where it happened, he calls his secretary, Effie Perine, and gives her the instructions to tell Archer's widow, Iva, about her husband's death. When he finally gets back to his home, he is then accosted by two policemen, who ask him questions about the shooting of Archer and then also the shooting of Thursby, which happened after Archer was killed. 

This is of course just the start of an exciting and renowned detective novel where very little is as it appears to be, and where Miss Wonderly herself is shown to have a number of secrets, not least her name:

The hell of it, Miss--Is your name Wonderly or Leblanc?' She blushed and murmured: 'It's really O'Shaughnessy-- Brigid O'Shaughnessy.'

Note how the quote suggests the multiple identities of Miss Wonderly. The first two chapters however serve to introduce the main characters and the mystery that Sam Spade will then spend the rest of the novel uncovering, as his name suggests.