The painting is titled "Oedipus and the Sphinx" and was created by Gustave Moreau in 1864.
The mythological being depicted on the left-hand side of the painting is the Sphinx.
It depicts the encounter between Oedipus and the Sphinx at the crossroads on Oedipus's journey between Thebes and Delphi. In the myth, Oedipus must answer the Sphinx's riddle correctly in order to pass.
The riddle posed by the Sphinx is: "What walks on four feet in the morning, two in the afternoon and three at night?" Oedipus correctly answers, "Man: as an infant, he crawls on all fours; as an adult, he walks on two legs; and in old age, he uses a cane as a third leg." This answer causes the Sphinx to destroy herself, and Oedipus is able to continue his journey