Short answers, pulled from the story.
The Battle of Pharsalus was fought on the 9th of August 48 BC near Pharsalus in central Greece. The precise location of the battlefield remains debated, with scholars divided between a site south of the Enipeus River and one north of it, near the village now called Krini Larisas.
Julius Caesar commanded the Caesarian forces, while Gnaeus Pompeius Magnus (Pompey) led the army of the Roman Republic. Pompey's infantry was subdivided under Lentulus, Scipio, and Ahenobarbus, with Labienus in command of the cavalry. Mark Antony commanded Caesar's left flank.
Caesar fielded approximately 22,000 Roman legionaries in 80 cohorts across 8 legions, along with about 1,000 cavalry. Pompey commanded between 36,000 and 45,000 Roman infantry according to ancient sources, and between 5,000 and 7,000 cavalry, plus thousands of archers, slingers, and allied troops.
Caesar secretly formed a fourth infantry line behind his cavalry to counter Pompey's superior horsemen. When Pompey's cavalry charged and routed Caesar's horse, this hidden line used their pila as thrusting spears against the cavalry, causing a panic. With Pompey's cavalry broken and his left wing exposed, Caesar committed his veteran reserves and broke the Pompeian line.
Pompey fled his camp disguised as an ordinary citizen and sailed to Mytilene, then Cilicia, and finally Egypt seeking refuge. He was assassinated upon arrival in Egypt on the orders of Ptolemy XIII. Caesar reached Alexandria in pursuit on the 2nd of October 48 BC.
Paul K. Davis described the battle as taking Caesar to the pinnacle of power and effectively ending the Roman Republic. The decisive Caesarian victory caused Pompey's network of client kings and allied senators across the Roman world to shift allegiance to Caesar, isolating the Optimate faction and leaving it without sufficient allies to continue the civil war.