Bridge game (Symbol)
First of all, the main occasion is the murder of Mr. Shaitana, which happens during the bridge game. The murder investigation is based on trying to find out the features of the game of each player, and this is the way to realize who is the murderer. So, the game is like a symbol of murder and some features of the game symbolize the style of the murderer.
Tiger (Allegory)
Poirot compares the killer to a tiger, saying that he likes to look at the tigers, but he would not go in their cage. This references enters into a broader allegory, calling attention to the cruelty of human nature that is central to a story such as this.
Murder (Motif)
There is no doubt that murder is the motif of a detective story, because of the murder every other event is happening. It is the basis of everything, the reason of every deed. There are even more than one murder in the novel: every character has his own criminal past, everybody had killed and keep killing each other to protect themselves from the information other people know about them.
Psychology (Motif)
The novel is built on the psychological aspects of every person and every situation in which they are involved. Poirot tries to open the inner world of every suspect, to realize why they might do this murder and whether they have really done this. In the end, he himself reveals the real killer and shows that psychology can be more important in investigation than facts.