In Homer's The Odyssey, how do Books XIII through XVI unite the two strands of plot?
In Homer's epic tale, The Odyssey, we learn of Odysseus' adventures and trials after leaving the Trojan War. The war took ten years, and he has traveled for ten more since: he has been gone for twenty years—misdirected, taken prisoner, and hampered by the gods. His family has waited a very long time for his return.
Books Thirteen through Sixteen provide a bridge between the segment of the tale that deals with Odysseus' adventures and his reunion with his family. Even though Odysseus is peacefully transported to his homeland of Ithaca, there are still challenges for the hero to face. While he has been gone, his son, Telemachus, has grown up, and Penelope, though overrun by suitors wishing to take Odysseus' property and wife, has remained true to her husband's memory.
In Book Thirteen, Athene (in disguise) appears to Odysseus and helps him hide the treasure he has been given. She then reveals herself to him with her assurance that she has never abandoned him. She also provides Odysseus with information about his wife and the suitors that have overrun his home. She disguises him as a beggar so no one will know he has returned. She travels to Sparta to tell Telemachus that he needs to return home. As Athene has directed, Odysseus sets out to find Eumaeus his faithful swineherd.
In Book Fourteen, Odysseus comes upon Eumaeus' home. Eumaeus is very cautious about revealing any information about his master, though it is obvious he is still devoted to him, and Odysseus goes about testing him to gauge his loyalty.
In Book Fifteen, Athene has appeared to Telemachus in a dream, urging him to return home, but not revealing his father's presence there. (She also warns him of danger upon his arrival.) He lands on the island, rather in the port, and he travels on foot to see Eumaeus first. As his ship returns to port, there is a group of suitors prepared to assassinate him, but he has thwarted their plan by making a stop along the way as Athene instructed.
In the meantime, Euraemus tells "the beggar" the story of his life, that he was once a prince sold into slavery, and how well he was cared for by those who took him into their home.
In Book Sixteen, when Telemachus arrives, he and Eumaeus joyfully reunite. The young man asks the swineherd to Penelope so that she knows her son is home safe.
While Euraemus is away, Odysseus reveals his true identity only to his son, and they begin to develop a plan to rid his home of the treacherous men vying for Penelope's hand.
These four chapters bring the long-absent Odysseus home, enlighten him to the plight of his wife at the hands of the suitors, meets Eumaeus who is still loyal to him, is reunited with his son, and starts to plan how to liberate his family from this hoard of "locusts that feed upon his food, drink and other resources."
This bridge connects Odysseus (the hero fighting impossible odds with magical characters who can control him, monsters that try to kill him, and the gods—some of whom are very unhappy with Odysseus, e.g., Poseidon) and his adventures in the realm of the unlikely and mysterious, with the obstacles that men face from their own kind. Odysseus will again have to prove himself a hero, but the threats now come from human beings instead of the gods or magical creatures, and his goal is no longer to return home, but to be reunited with his family and to live in peace.