You can find a summary of this act, as well as the prologue and Acts II & III at the link below. Here is the summary of Act I:
Act 1 opens with Argan adding up his many doctor’s bills and ringing for the maid, Toinette, who reveals her impatience with Argan and goes to fetch his daughter, Angélique. Argan, who is a hypochondriac, then goes off to the bathroom while Angélique asks Toinette for advice about Cléante, the young man with whom she recently fell in love, and who has promised to ask for her hand in marriage. When Argan returns, Angélique is delighted to hear him tell her of a marriage he has arranged for her, until she discovers that she is betrothed not to Cléante but to Thomas Diafoirus, who is about to graduate from medical school. Toinette argues with Argan, but he threatens to put his daughter in a convent unless she marries Thomas, and he chases Toinette with a stick.
Argan’s second wife, Béline, enters and consoles him, and Argan calls for a notary to discuss his will, since he would like to leave all of his money to his wife. Toinette warns Angélique that her stepmother is trying to undermine her interests, but Angélique is only concerned that her father does not arrange for her to marry a man she loves. Toinette promises to send word to Cléante about the arranged marriage by talking to Punchinello, an old moneylender. The scene then shifts to the ‘‘First Interlude,’’ in which Punchinello sings his lover a serenade, until he is interrupted by an old woman, a chorus of violins, and then a group of archers, who he bribes to avoid being arrested.