Short answers, pulled from the story.
The Greco-Italian War began on the 28th of October 1940, when Italy invaded Greece from Albania following Metaxas's rejection of Mussolini's ultimatum. It ended on the 23rd of April 1941, when Greece surrendered to Italy, after surrendering to Germany on the 20th of April.
Mussolini invaded Greece as part of his ambition to dominate the Mediterranean-Balkan region and secure Italian "spazio vitale" before Germany won the war against Britain. He was also furious that Hitler had sent troops into Romania without informing him, and saw a quick victory over Greece as a way to assert Italian equality with Germany. Foreign Minister Ciano's personal ambitions and manipulation - including fabricating the story of the bandit Daut Hoxha - accelerated Mussolini's decision.
The Italian invasion failed. Greek forces stopped the advance within Greek territory by mid-November 1940 and then counter-attacked, driving the Italians back into Albania and capturing Korçë on the 22nd of November and the Klisura Pass in January 1941. The Greeks' success was called the "first Axis setback of the entire war" by historian Mark Mazower. Greece was ultimately defeated only after Germany invaded on the 6th of April 1941.
The Greek light cruiser Elli was sunk by the Italian submarine Delfino on the 15th of August 1940, while at anchor in Tinos harbour during a major Greek religious holiday. The attack was ordered by Mussolini and navy chief Domenico Cavagnari. The Greek government announced the attacker was of unknown nationality, but the sinking outraged the Greek people and strengthened their resolve to resist.
The Italian army suffered 102,064 combat casualties, including 13,755 dead, 3,900 missing, and fifty thousand wounded. Greek forces suffered over 83,500 combat casualties, including 13,325 killed and 1,200 missing, with 42,000 wounded.
Ioannis Metaxas was the Prime Minister and dictator of Greece, leader of the 4th of August Regime that came to power in 1936. He rejected Mussolini's ultimatum on the 28th of October 1940 with the words "Alors, c'est la guerre," sparking the war. Though personally pessimistic about Greece's chances, he had prepared the country's defenses and maintained alignment with Britain throughout the conflict.