Early in Homer's Odyssey, Telemachus is inspired by Athene (also spelled Athena) to make a journey in search of his father, who has been away from home for 20 years. One of the reasons for this journey is that Odysseus' palace is infested with suitors, who, believing that Odysseus is dead, want to marry Odysseus' wife Penelope.
One of the most prominent suitors is Antinous, whose name means "the opposing mind" (an appropriate name for an enemy). The other suitor identified as one of the leaders is Eurymachus.
Homer describes the suitors' reaction to Telemachus' journey at 2.296-336. Near the end of Odyssey 4, the suitors set a trap for Telemachus, who was returning from his journey, and plotted "secretly to murder Telemachus" (A.S. Kline translation).
Fortunately for Telemachus, he manages to avoid the trap set by the suitors. Homer, however, keeps the audience in suspense and we do not learn that Telemachus has made it safely home until 16.321-392.
For a complete list of the suitors, see Odyssey 16.213-257.