Short answers, pulled from the story.
Filippo Brunelleschi is best known for designing the dome of the Florence Cathedral, Santa Maria del Fiore, completed in 1436. He is also credited with establishing the mathematical system of linear perspective that governed pictorial depictions of space until the late 19th century, and is considered a founding father of Renaissance architecture.
Brunelleschi built the dome using two shells, one inside the other, so the inner dome bore the structural load without requiring external support. He employed a herringbone brick-laying pattern known as opus spicatum, used wooden and sandstone chains as tensioning rings around the base, and invented a new hoisting machine to raise the masonry. More than four million bricks were used in the octagonal structure.
Brunelleschi received his patent in 1421, making him the first person to receive a patent in the Western world. The patent covered a river transport vessel designed to carry marble along the River Arno more cheaply than existing methods.
Lorenzo Ghiberti was Brunelleschi's main rival in the 1401 competition for the bronze doors of the Florence Baptistery. The jury could not choose between their panels and proposed a collaboration; Brunelleschi refused to share control and let Ghiberti take the commission alone. The two competed again in 1418 for the dome project and in 1436 for the dome's lantern, with Brunelleschi winning both.
Il Badalone, the large boat Brunelleschi built in 1427 to transport marble from Pisa to Florence along the River Arno, sank on its maiden voyage. The sinking also took a sizable portion of Brunelleschi's personal fortune.
Brunelleschi is buried in the crypt of the Cathedral of Florence, Santa Maria del Fiore, the same building whose dome defined his career. A marble bust said to be carved from life was placed there, and a statue of him was later erected in the square in front of the cathedral, facing upward toward the dome.