You cannot analyse a play you cannot follow, so get the plot of An Inspector Calls straight first. The action happens in one room, in real time, over a single evening, which makes it fast and tight. Here is the whole story in plain English, act by act. Because the play is in copyright, I quote only short lines here; use your copy of the script for the full text.
Act 1: the engagement and the Inspector
The Birling family are at dinner in 1912, celebrating the engagement of their daughter Sheila to Gerald Croft. Mr Birling, a wealthy factory owner, makes confident speeches about how there will be no war and how the Titanic is 'unsinkable', and lectures the young men that a man should 'look after himself and his own'. Just then a police inspector, Goole, arrives to investigate the suicide of a young woman, Eva Smith, who died after drinking disinfectant.
The Inspector reveals the first links in a chain. Mr Birling had sacked Eva from his factory two years earlier for helping to lead a strike for slightly higher wages. Then Sheila, in a fit of jealous temper, had her dismissed from her next job at a shop. Sheila is immediately, genuinely ashamed.
Act 2: Gerald and Mrs Birling
The Inspector turns to Gerald, and it emerges that he had kept Eva, who was by then calling herself Daisy Renton, as his mistress before ending the affair. Sheila, though hurt, respects his honesty and hands back the engagement ring. Then Mrs Birling is questioned. As chair of a women's charity, she had recently refused help to a pregnant, desperate Eva, and she coldly insists the girl 'had only herself to blame' and that the father of the child should be made responsible, not knowing who he is.
Act 3: Eric and the Inspector's warning
The last confession is Eric's. He got Eva pregnant, and he had stolen money from his father's firm to support her. The horror lands doubly, because it means Mrs Birling, in refusing Eva and demanding the father be punished, had condemned her own son and unborn grandchild. The Inspector delivers his final warning, that if people do not learn they are 'responsible for each other', they will be taught it 'in fire and blood and anguish', and leaves.
Shaken, the family begin to doubt him. Gerald discovers that no Inspector Goole works for the local police, and a phone call to the infirmary confirms no girl has died there that night. The older Birlings and Gerald relax, delighted it was a hoax, while Sheila and Eric insist the lesson still stands. Then the telephone rings: a girl has just died on her way to the infirmary, and a police inspector is on his way to ask some questions. The play ends on that chilling twist.
With the story clear, go deeper on the characters, learn the lines on the key quotes page, and understand the world of the play on the context page.