Starting around the First Dynasty, Egyptians buried their dead in an undeground chamber, and covered it with a mastaba. A mastaba is a low structure, rectangular in plan, with inward-sloping walls and a flat roof.
a mastaba, source
Sometime around the Third Dynasty, King Zoser decided he wanted something different to mark his tomb. He hired the architect Imhotep to design him something good, and Imhotep delivered (back then, architects were the designer and the actual builder... I'm sure glad things have changed.) Imhotep decided to take the mastaba a step further and stack them towards the heavens. In doing so, he created the first pyramidal shape in the 6-tiered Step Pyramid at Saqqara.
King Zoser's Step Pyramid
6 mastabas make up the Step Pyramid
As the first king of the Fourth Dynasty, King Sneferu saw what Zoser had done and wanted to improve it by filling in the "steps" and making the first attempt at the classic pyramidal shape. His architects set to work...however they had the angle calculated wrong. They realized when they were a good ways up that the angle couldn't support itself and the structure would fail. Too late to turn back, they just changed the angle midway and continued on. Thus we have the Bent Pyramid at Darshur.
The Bent Pyramid and Red Pyramid
The Bent Pyramid
The Bent Pyramid still has much of it's outer limestone casing
Building on the construction knowledge learned from the Step and Bent Pyramids, King Snefuru decided to try one more time...and this time succeeded in building the first successful true pyramid; the Red Pyramid. The Red Pyramid is 341 feet high and is likely called the "red" pyramid because of it's reddish limestone interiors.
The Red Pyramid
The Red Pyramid - third time's a charm
King Khufu, the son of Sneferu learned from his father's eventual success, moved the royal acropolis to Giza, and created the Great Pyramid for himself. The Great Pyramid is 481 feet tall, and is the largest pyramid ever built!
The Pyramids at Giza - the Great Pyramid is far left
King Khufu used the best stone in the quarry for his pyramid
The Great Pyramid
Khufu's son, King Kahfre also built his pyramid at the Giza acropolis near his father's. Kahfre's pyramid is smaller, but he built it on a higher elevation and also added the Great Sphinx. Some of the limestone casing is still visible on this pyramid.
Pyramid of Khafre with the Sphinx
Smaller still is Kahfre's son's pyramid, the Pyramid of Menkaure, the last of the three Great Pyramids at Giza. Maybe the quarry was out of limestone, or maybe they just ran out of time, but Menkaure's Pyramid is only 213 feet high.
The Pyramid of Menkaure with the city of Cairo in the distance