Short answers, pulled from the story.
Huygens discovered Titan, Saturn's largest moon, on the 25th of March 1655. He also became the first person to correctly explain Saturn's unusual telescopic appearance, describing it as surrounded by a thin, flat ring, nowhere touching, and inclined to the ecliptic, which he published in Systema Saturnium in 1659.
Christiaan Huygens invented and patented the pendulum clock in 1657. It was manufactured by Salomon Coster in The Hague and remained the most accurate timekeeper in the world for almost three hundred years until the 1930s.
Huygens proposed that light travels as radiating wavefronts, with each point along a wavefront emitting its own spherical wave. He published this theory in 1690 as the Traité de la Lumière. Augustin-Jean Fresnel extended the theory in 1821, explaining birefringence by treating light as a transverse wave, and the resulting framework became known as the Huygens-Fresnel principle.
Horologium Oscillatorium, published in 1673, is considered one of the most important seventeenth-century works on mechanics. It is the first modern scientific work to idealize a physical problem using mathematical parameters. In it, Huygens solved the tautochrone problem, derived the formula for a pendulum's period, developed the theory of evolutes, and described the phenomenon now called entrainment.
Huygens published De Ratiociniis in Ludo Aleae in 1657, the most coherent mathematical treatment of games of chance written to that date. He extended Pascal's concept of a fair game into a non-standard theory of expected values, and his five challenge problems at the end of the book were used as the standard test of mathematical skill in probability for the next sixty years, influencing Abraham de Moivre, Jacob Bernoulli, and Leibniz.
In Cosmotheoros, published posthumously in 1698, Huygens argued that liquid water is essential for life and must vary in properties from planet to planet. He interpreted dark and bright spots on Mars and Jupiter as evidence of water and ice, and estimated stellar distances using a hole-in-a-screen technique that compared sunlight brightness to that of Sirius.